scholarly journals Evolution of sub-spaces at high and low energies

2019 ◽  
Vol 79 (11) ◽  
Author(s):  
Arkady A. Popov ◽  
Sergey G. Rubin
Keyword(s):  
Energy Range ◽  
Crucial Role ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Quantum Corrections ◽  
Extra Space ◽  
High Energies ◽  
Low Energies ◽  
Higher Derivatives ◽  
Shed Light

Abstract The evolution of sub-spaces in the framework of gravity with higher derivatives is studied. Numerical solutions to exact differential equations are found. It is shown that the initial conditions play crucial role in the space dynamic. Appropriate metrics describing an expanding and a stationary sub-space shed light on the well-known question: why our 3-dim space is large but an extra space is small and stable (if exists)? It is assumed that the values of parameters at high energies strongly depend on uncontrolled quantum corrections and, hence, are not equal to their values at low energies. Therefore, there is no way to trace solutions throughout the energy range, and we restrict ourselves to the sub-Planckian and the inflationary energies.

scholarly journals Hydrodynamics of flagellated microswimmers near free-slip interfaces

2016 ◽  
Vol 789 ◽  
pp. 514-533 ◽  
Author(s):  
D. Pimponi ◽  
M. Chinappi ◽  
P. Gualtieri ◽  
C. M. Casciola
Keyword(s):  
Numerical Solutions ◽  
Stokes Equations ◽  
Slip Surface ◽  
Initial Conditions ◽  
Aerobic Bacteria ◽  
Slip Boundary ◽  
Experimental Findings ◽  
Micro Organisms ◽  
Air Interfaces ◽  
Shed Light

The hydrodynamics of a flagellated micro-organism is investigated when swimming close to a planar free-slip surface by means of numerical solutions of the Stokes equations obtained via a boundary element method. Depending on the initial conditions, the swimmer can either escape from the free-slip surface or collide with the boundary. Interestingly, the micro-organism does not exhibit a stable orbit. Independently of escape or attraction to the interface, close to a free-slip surface, the swimmer follows a counter-clockwise trajectory, in agreement with experimental findings (Di Leonardo et al., Phys. Rev. Lett., vol. 106 (3), 2011, 038101). The hydrodynamics is indeed modified by the free surface. In fact, when the same swimmer moves close to a no-slip wall, a set of initial conditions exists which result in stable orbits. Moreover, when moving close to a free-slip or a no-slip boundary, the swimmer assumes a different orientation with respect to its trajectory. Taken together, these results contribute to shed light on the hydrodynamical behaviour of micro-organisms close to liquid–air interfaces which are relevant for the formation of interfacial biofilms of aerobic bacteria.

scholarly journals Inhomogeneous Extra Space as a Tool for the Top-Down Approach

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Sergey G. Rubin
Keyword(s):  
Cosmological Constant ◽  
Dimensional Space ◽  
Quantum Corrections ◽  
Top Down ◽  
Extra Space ◽  
High Energies

The top-down approach for the 6-dimensional space has been elaborated. The connection between the cosmological constant and the extra space metric has been obtained. The metric can be found with the necessary accuracy. It is shown that descent from high energies to the low ones leads to the quantum corrections which influence weakly the metric of extra space.

Direct collection of some metal ions in an electromagnetic isotope separator and related surface effects

1969 ◽  
Vol 47 (21) ◽  
pp. 2405-2414 ◽  
Author(s):  
A. Fontell ◽  
E. Arminen
Keyword(s):  
Energy Range ◽  
Metal Ions ◽  
Metal Atom ◽  
The Self ◽  
Isotope Separator ◽  
Graphite Block ◽  
High Energies ◽  
Metal Atoms ◽  
Saturation Region ◽  
Low Energies

The direct collection of Fe, Co, Ni, Cu, Zn, and Sn ions has been investigated in the energy range from about 10 eV to 110 keV in an electromagnetic isotope separator. At low energies the ions build up a layer on the surface of the graphite block used as a backing, while at high energies only a certain saturation value can be collected. For these ions the highest energies at which the building-up of a layer was observed were 1.5 keV, 1.0 keV, 0.8 keV, 0.3 keV, 0.3 keV, and 0.45 keV, respectively. In the building-up region the efficiency of the collection process and the sticking probability of ions as a function of energy have been measured. From these the self-sputtering ratios have been calculated. In the saturation region the amounts of material collected have been measured and the ranges of ions in graphite backings saturated with metal atoms have been calculated theoretically. This calculation gives an estimate of the metal atom concentrations in the graphite, which in turn determines the sputtering ratio of carbon.

Oscillatory flow past a circular cylinder in a rotating frame

1997 ◽  
Vol 345 ◽  
pp. 101-131
Author(s):  
M. D. KUNKA ◽  
M. R. FOSTER
Keyword(s):  
Circular Cylinder ◽  
Steady Flow ◽  
Stagnation Point ◽  
Oscillatory Flow ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Temporal Integration ◽  
Oncoming Flow ◽  
Flow Past ◽  
Rear Stagnation Point

Because of the importance of oscillatory components in the oncoming flow at certain oceanic topographic features, we investigate the oscillatory flow past a circular cylinder in an homogeneous rotating fluid. When the oncoming flow is non-reversing, and for relatively low-frequency oscillations, the modifications to the equivalent steady flow arise principally in the ‘quarter layer’ on the surface of the cylinder. An incipient-separation criterion is found as a limitation on the magnitude of the Rossby number, as in the steady-flow case. We present exact solutions for a number of asymptotic cases, at both large frequency and small nonlinearity. We also report numerical solutions of the nonlinear quarter-layer equation for a range of parameters, obtained by a temporal integration. Near the rear stagnation point of the cylinder, we find a generalized velocity ‘plateau’ similar to that of the steady-flow problem, in which all harmonics of the free-stream oscillation may be present. Further, we determine that, for certain initial conditions, the boundary-layer flow develops a finite-time singularity in the neighbourhood of the rear stagnation point.

Key words: Nonlinear Differential-Difference Equations; Exp-Function Method; N-Soliton Solutions

2010 ◽  
Vol 65 (11) ◽  
pp. 935-949 ◽  
Author(s):  
Mehdi Dehghan ◽  
Jalil Manafian ◽  
Abbas Saadatmandi
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Homotopy Analysis Method ◽  
Fractional Derivatives ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Analysis Method ◽  
Partial Differential ◽  
Integer Order ◽  
Homotopy Analysis

In this paper, the homotopy analysis method is applied to solve linear fractional problems. Based on this method, a scheme is developed to obtain approximation solution of fractional wave, Burgers, Korteweg-de Vries (KdV), KdV-Burgers, and Klein-Gordon equations with initial conditions, which are introduced by replacing some integer-order time derivatives by fractional derivatives. The fractional derivatives are described in the Caputo sense. So the homotopy analysis method for partial differential equations of integer order is directly extended to derive explicit and numerical solutions of the fractional partial differential equations. The solutions are calculated in the form of convergent series with easily computable components. The results of applying this procedure to the studied cases show the high accuracy and efficiency of the new technique.

scholarly journals Numerical daemons of hydrological models are summoned by extreme precipitation

2021 ◽  
Author(s):  
Peter T. La Follette ◽  
Adriaan J. Teuling ◽  
Nans Addor ◽  
Martyn Clark ◽  
Koen Jansen ◽  
...  
Keyword(s):  
Numerical Methods ◽  
Extreme Precipitation ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Computational Cost ◽  
Numerical Error ◽  
Hydrological Models ◽  
Multiple Model ◽  
Numerical Techniques ◽  
Modeling Framework

Abstract. Hydrological models are usually systems of nonlinear differential equations for which no analytical solutions exist and thus rely on approximate numerical solutions. While some studies have investigated the relationship between numerical method choice and model error, the extent to which extreme precipitation like that observed during hurricanes Harvey and Katrina impacts numerical error of hydrological models is still unknown. This knowledge is relevant in light of climate change, where many regions will likely experience more intense precipitation events. In this experiment, a large number of hydrographs is generated with the modular modeling framework FUSE, using eight numerical techniques across a variety of forcing datasets. Multiple model structures, parameter sets, and initial conditions are incorporated for generality. The computational expense and numerical error associated with each hydrograph were recorded. It was found that numerical error (root mean square error) usually increases with precipitation intensity and decreases with event duration. Some numerical methods constrain errors much more effectively than others, sometimes by many orders of magnitude. Of the tested numerical methods, a second-order adaptive explicit method is found to be the most efficient because it has both low numerical error and low computational cost. A basic literature review indicates that many popular modeling codes use numerical techniques that were suggested by this experiment to be sub-optimal. We conclude that relatively large numerical errors might be common in current models, and because these will likely become larger as the climate changes, we advocate for the use of low cost, low error numerical methods.

Electron Energy Dependence of Amorphization in Zr3Fe

1993 ◽  
Vol 316 ◽  
Author(s):  
A.T. Motta ◽  
L.M. Howe ◽  
P.R. Okamoto
Keyword(s):  
Electron Energy ◽  
Cross Section ◽  
Sharp Increase ◽  
Low Dose ◽  
National Laboratory ◽  
Argonne National Laboratory ◽  
High Energies ◽  
Intermediate Energies ◽  
Low Energies ◽  
Order Of Magnitude

ABSTRACTThis paper reports the results from a study conducted to determine the effect of electron energy on the dose-to-amorphization of Zr3Fe at 23-30 K. Zr3Fe samples were irradiated in the HVEM at Argonne National Laboratory, at energies ranging from 200 to 900 keV. Amorphization occurred at electron energies from 900 keV down to 250 keV. Three distinct regions were observed: between 900 and 700 keV amorphization occurred at a constant low dose of ~ 4 × 1021 e cm-2; a higher plateau at 1022 was observed between 600 and 400 keV, and finally there was a sharp increase in the dose-to-amorphization below 400 keV, so that at 250 keV the necessary dose was an order of magnitude higher than that at 900 keV. In the region below 400 keV there was evidence of a dependence of the dose-to-amorphization on the orientation of the sample with respect to the electron beam. The results can be analyzed in terms of a composite displacement cross section dominated at high energies by displacements of Zr and Fe atoms, by displacements of Fe atoms at intermediate energies and of secondary displacements of lattice atoms by recoil impurities at low energies.

Effects of geometric similarity ratio on the disturbance amplitude of shock-wave front in viscosity measurement

2021 ◽  
pp. 2150330
Author(s):  
Kai Yang ◽  
Quan-Yu Xu ◽  
Xiao Wu ◽  
Xiao-Juan Ma
Keyword(s):  
Shock Wave ◽  
Phase Shift ◽  
Wave Front ◽  
Shock Wave Front ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Viscosity Measurement ◽  
Geometric Similarity ◽  
Similarity Ratio ◽  
Simulation Results

Geometric similarity ratio is one of the important factors that affects the disturbance amplitude of shock-wave front in viscosity measurement. In this paper, the Euler difference scheme of two-dimensional (2D) equations of viscous fluid mechanics is used to simulate the disturbance amplitude damping curves under different geometric similarity ratios, and the corresponding numerical solutions are shown. The samples of aluminum shocked to 80 GPa are taken as an example. The simulation results show that the initial conditions, material viscosity, wavelength, and sample geometric similarity ratio affect the evolution of the shock front sine wave disturbance. For flyer-impact flow field, the phase shift increases from 0 to a certain value with the viscosity coefficient for sample with wavelength [Formula: see text] mm and geometric similarity ratio [Formula: see text], 0.1. So, the geometric similarity method can be used to measure the viscosity of material. But it is found that the phase shift is sensitive to the geometric similarity ratio, which should be considered in Zaidel’s equation. So, some flyer-impact experiments will be carried out to determine the simulation results, and find the quantity relation of phase shift and viscosity of material in the future investigation.

scholarly journals A Numerical Algorithm for the Solutions of ABC Singular Lane–Emden Type Models Arising in Astrophysics Using Reproducing Kernel Discretization Method

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 923 ◽  
Author(s):  
Omar Abu Arqub ◽  
Mohamed S. Osman ◽  
Abdel-Haleem Abdel-Aty ◽  
Abdel-Baset A. Mohamed ◽  
Shaher Momani
Keyword(s):  
Convergence Analysis ◽  
Fractional Order ◽  
Numerical Algorithm ◽  
Reproducing Kernel ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Discretization Method ◽  
Fractional Models ◽  
Discretization Technique ◽  
And Mathematics

This paper deals with the numerical solutions and convergence analysis for general singular Lane–Emden type models of fractional order, with appropriate constraint initial conditions. A modified reproducing kernel discretization technique is used for dealing with the fractional Atangana–Baleanu–Caputo operator. In this tendency, novel operational algorithms are built and discussed for covering such singular models in spite of the operator optimality used. Several numerical applications using the well-known fractional Lane–Emden type models are examined, to expound the feasibility and suitability of the approach. From a numerical viewpoint, the obtained results indicate that the method is intelligent and has several features stability for dealing with many fractional models emerging in physics and mathematics, using the new presented derivative.

New Travelling Wave Solutions of Burgers Equation with Finite Transport Memory

2010 ◽  
Vol 65 (8-9) ◽  
pp. 633-640 ◽  
Author(s):  
Rathinasamy Sakthivel ◽  
Changbum Chun ◽  
Jonu Lee
Keyword(s):  
Evolution Equations ◽  
Numerical Solutions ◽  
Burgers Equation ◽  
Diffusion Processes ◽  
Initial Conditions ◽  
Travelling Wave ◽  
Nonlinear Evolution Equations ◽  
Wave Solutions ◽  
Wide Range ◽  
Finite Memory

The nonlinear evolution equations with finite memory have a wide range of applications in science and engineering. The Burgers equation with finite memory transport (time-delayed) describes convection-diffusion processes. In this paper, we establish the new solitary wave solutions for the time-delayed Burgers equation. The extended tanh method and the exp-function method have been employed to reveal these new solutions. Further, we have calculated the numerical solutions of the time-delayed Burgers equation with initial conditions by using the homotopy perturbation method (HPM). Our results show that the extended tanh and exp-function methods are very effective in finding exact solutions of the considered problem and HPM is very powerful in finding numerical solutions with good accuracy for nonlinear partial differential equations without any need of transformation or perturbation

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