scholarly journals Analytical theory in terms of J2, J3, J4 with eccentric anomaly for short-term orbit predictions using uniformly regular KS canonical elements

2019 ◽  
Vol 7 (1) ◽  
pp. 1 ◽  
Author(s):  
Athira Anand P ◽  
Ram Krishan Sharma
Keyword(s):  
Initial Conditions ◽  
Equations Of Motion ◽  
Radial Distance ◽  
Analytical Theory ◽  
Short Term ◽  
Eccentric Anomaly ◽  
Regular Elements ◽  
Wide Range ◽  
Space Objects ◽  
Uniformly Regular

A new non-singular analytical theory with respect to the Earth’s zonal harmonic terms J2, J3, J4 has been developed for short-periodic motion, by analytically integrating the uniformly regular KS canonical equations of motion using generalized eccentric anomaly ‘E’ as the independent variable. Only one of the eight equations need to be integrated analytically to generate the state vector, due to the symmetry in the equations of motion, and the computation for the other equations is done by changing the initial conditions. King-Hele’s expression for radial distance ‘r’ with J2 is also considered in generating the solution. The results obtained from the analytical expressions in a single step during half a revolution match quite well with numerically integrated values. Numerical results also indicate that the solution is reasonably accurate for a wide range of orbital elements during half a revolution and is an improvement over Sharon et al. [17] theory, which is generated in terms of KS regular elements. It can be used for studying the short-term relative motion of two or more space objects and in collision avoidance studies of space objects. It can be also useful for onboard computation in the navigation and guidance packages.  

scholarly journals Visualization of Transition's Scenarios from Harmonic to Chaotic Flexible Nonlinear-elastic Nano Beam's Oscillations

2019 ◽  
Author(s):  
Вадим Крысько ◽  
Vadim Krys'ko ◽  
Ирина Папкова ◽  
Irina Papkova ◽  
Екатерина Крылова ◽  
...  
Keyword(s):  
Cauchy Problem ◽  
Differential Equations ◽  
Initial Conditions ◽  
Couple Stress Theory ◽  
Equations Of Motion ◽  
Nonlinear Partial Differential Equations ◽  
Physical Nonlinearity ◽  
Variable Load ◽  
Wide Range ◽  
The Cauchy Problem

In this study, a mathematical model of the nonlinear vibrations of a nano-beam under the action of a sign-variable load and an additive white noise was constructed and visualized. The beam is heterogeneous, isotropic, elastic. The physical nonlinearity of the nano-beam was taken into account. The dependence of stress intensity on deformations intensity for aluminum was taken into account. Geometric non-linearity according to Theodore von Karman’s theory was applied. The equations of motion, the boundary and initial conditions of the Hamilton-Ostrogradski principle with regard to the modified couple stress theory were obtained. The system of nonlinear partial differential equations to the Cauchy problem by the method of finite differences was reduced. The Cauchy problem by the finite-difference method in the time coordinate was solved. The Birger variable method was used. Data visualization is carried out from the standpoint of the qualitative theory of differential equations and nonlinear dynamics were carried out. Using a wide range of tools visualization allowed to established that the transition from ordered vibrations to chaos is carried out according to the scenario of Ruelle-Takens-Newhouse. With an increase of the size-dependent parameter, the zone of steady and regular vibrations increases. The transition from regular to chaotic vibrations is accompanied by a tough dynamic loss of stability. The proposed method is universal and can be extended to solve a wide class of various problems of mechanics of shells.

scholarly journals On the generation of internal waves by river plumes in subcritical initial conditions

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
R. Mendes ◽  
J. C. B. da Silva ◽  
J. M. Magalhaes ◽  
B. St-Denis ◽  
D. Bourgault ◽  
...  
Keyword(s):  
Numerical Modeling ◽  
Internal Waves ◽  
Coastal Waters ◽  
Initial Conditions ◽  
Spatial Scales ◽  
River Plumes ◽  
Wide Range ◽  
Near Shore ◽  
Generation Mechanisms ◽  
Douro River

AbstractInternal waves (IWs) in the ocean span across a wide range of time and spatial scales and are now acknowledged as important sources of turbulence and mixing, with the largest observations having 200 m in amplitude and vertical velocities close to 0.5 m s−1. Their origin is mostly tidal, but an increasing number of non-tidal generation mechanisms have also been observed. For instance, river plumes provide horizontally propagating density fronts, which were observed to generate IWs when transitioning from supercritical to subcritical flow. In this study, satellite imagery and autonomous underwater measurements are combined with numerical modeling to investigate IW generation from an initial subcritical density front originating at the Douro River plume (western Iberian coast). These unprecedented results may have important implications in near-shore dynamics since that suggest that rivers of moderate flow may play an important role in IW generation between fresh riverine and coastal waters.

scholarly journals The Impact of Initial Conditions in N-Body Simulations of Debris Discs

2015 ◽  
Vol 32 ◽  
Author(s):  
E. Thilliez ◽  
S. T. Maddison
Keyword(s):  
Numerical Simulations ◽  
Initial Conditions ◽  
Parent Body ◽  
Dust Trapping ◽  
Physical Context ◽  
Disc Width ◽  
Wide Range ◽  
Belt Width ◽  
New Generation ◽  
The Impact

AbstractNumerical simulations are a crucial tool to understand the relationship between debris discs and planetary companions. As debris disc observations are now reaching unprecedented levels of precision over a wide range of wavelengths, an appropriate level of accuracy and consistency is required in numerical simulations to confidently interpret this new generation of observations. However, simulations throughout the literature have been conducted with various initial conditions often with little or no justification. In this paper, we aim to study the dependence on the initial conditions of N-body simulations modelling the interaction between a massive and eccentric planet on an exterior debris disc. To achieve this, we first classify three broad approaches used in the literature and provide some physical context for when each category should be used. We then run a series of N-body simulations, that include radiation forces acting on small grains, with varying initial conditions across the three categories. We test the influence of the initial parent body belt width, eccentricity, and alignment with the planet on the resulting debris disc structure and compare the final peak emission location, disc width and offset of synthetic disc images produced with a radiative transfer code. We also track the evolution of the forced eccentricity of the dust grains induced by the planet, as well as resonance dust trapping. We find that an initially broad parent body belt always results in a broader debris disc than an initially narrow parent body belt. While simulations with a parent body belt with low initial eccentricity (e ~ 0) and high initial eccentricity (0 < e < 0.3) resulted in similar broad discs, we find that purely secular forced initial conditions, where the initial disc eccentricity is set to the forced value and the disc is aligned with the planet, always result in a narrower disc. We conclude that broad debris discs can be modelled by using either a dynamically cold or dynamically warm parent belt, while in contrast eccentric narrow debris rings are reproduced using a secularly forced parent body belt.

scholarly journals Harmonic hybrid inflation

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Federico Carta ◽  
Nicole Righi ◽  
Yvette Welling ◽  
Alexander Westphal
Keyword(s):  
Domain Wall ◽  
Symmetry Breaking ◽  
Initial Conditions ◽  
Scalar Potential ◽  
Field Range ◽  
Slow Roll ◽  
Minimal Form ◽  
Wide Range ◽  
Hybrid Inflation ◽  
Type Iib String Theory

Abstract We present a mechanism for realizing hybrid inflation using two axion fields with a purely non-perturbatively generated scalar potential. The structure of the scalar potential is highly constrained by the discrete shift symmetries of the axions. We show that harmonic hybrid inflation generates observationally viable slow-roll inflation for a wide range of initial conditions. This is possible while accommodating certain UV arguments favoring constraints f ≲ MP and ∆ϕ60 ≲ MP on the axion periodicity and slow-roll field range, respectively. We discuss controlled ℤ2-symmetry breaking of the adjacent axion vacua as a means of avoiding cosmological domain wall problems. Including a minimal form of ℤ2-symmetry breaking into the minimally tuned setup leads to a prediction of primordial tensor modes with the tensor-to-scalar ratio in the range 10−4 ≲ r ≲ 0.01, directly accessible to upcoming CMB observations. Finally, we outline several avenues towards realizing harmonic hybrid inflation in type IIB string theory.

Effects of Atovaquone on the Ultrastructural Morphology of Pneumocystis Carinii

1997 ◽  
Vol 3 (S2) ◽  
pp. 81-82
Author(s):  
M.P. Goheen ◽  
M.S. Bartlett ◽  
M.M. Shaw ◽  
S.R. Meshnick ◽  
J.W. Smith
Keyword(s):  
Adverse Reactions ◽  
Pneumocystis Carinii ◽  
Spinner Flask ◽  
Short Term ◽  
Human Embryonic Lung ◽  
Transmission Electron ◽  
Significant Incidence ◽  
Wide Range ◽  
Acquired Immunodeficiency ◽  
Immunodeficiency Syndrome

Pneumocystis carinii pneumonia (PCP) occurs at some time in most patients with acquired immunodeficiency syndrome (AIDS). Trimethoprim/sulfamethoxazole or pentamidine isothionate are the traditional modes of therapy for treatment and prophylaxis of PCP. Unfortunately these drugs are associated with a significant incidence of adverse side effects particularly in patients with AIDS. Toxicity and a growing concern that P. carinii strains are becoming resistant to these compounds is providing the impetus for the search for additional drugs to combat P. carinii. Atovaquone, developed as an antimalarial agent, has activity against a wide range of other organisms, including Toxoplasma sp. and P. carinii, with a lower incidence of adverse reactions during clinical trials. Atovaquone inhibits mitochondrial respiration in P. falciparum and P. carinii. In this study transmission electron microscopy (TEM) was used to observe the effects of atovaquone on P. carinii organisms in short term spinner flask culture.Spinner flask cultures of human embryonic lung cells were inoculated with P. carinii from infected rat lung.

Numerical investigation of the propagation of shock waves in rigid porous materials: development of the computer code and comparison with experimental results

1996 ◽  
Vol 324 ◽  
pp. 163-179 ◽  
Author(s):  
A. Levy ◽  
G. Ben-Dor ◽  
S. Sorek
Keyword(s):  
Porous Materials ◽  
Initial Conditions ◽  
Computer Code ◽  
Experimental Results ◽  
Numerical Code ◽  
Materials Development ◽  
Numerical Predictions ◽  
Wide Range ◽  
Dimensional Version ◽  
The One

The governing equations of the flow field which is obtained when a thermoelastic rigid porous medium is struck head-one by a shock wave are developed using the multiphase approach. The one-dimensional version of these equations is solved numerically using a TVD-based numerical code. The numerical predictions are compared to experimental results and good to excellent agreements are obtained for different porous materials and a wide range of initial conditions.

scholarly journals Jet-Surface Interaction Test: Far-Field Noise Results

2013 ◽  
Vol 135 (7) ◽  
Author(s):  
Clifford A. Brown
Keyword(s):  
High Speed ◽  
Radial Distance ◽  
Jet Noise ◽  
Surface Interaction ◽  
Shielding Effect ◽  
Noise Prediction ◽  
Far Field ◽  
Wide Range ◽  
Field Noise ◽  
Surface Length

Many configurations proposed for the next generation of aircraft rely on the wing or other aircraft surfaces to shield the engine noise from the observers on the ground. However, the ability to predict the shielding effect and any new noise sources that arise from the high-speed jet flow interacting with a hard surface is currently limited. Furthermore, quality experimental data from jets with surfaces nearby suitable for developing and validating noise prediction methods are usually tied to a particular vehicle concept and, therefore, very complicated. The Jet-Surface Interaction Tests are intended to supply a high quality set of data covering a wide range of surface geometries and positions and jet flows to researchers developing aircraft noise prediction tools. The initial goal is to measure the noise of a jet near a simple planar surface while varying the surface length and location in order to: (1) validate noise prediction schemes when the surface is acting only as a jet noise shield and when the jet-surface interaction is creating additional noise, and (2) determine regions of interest for future, more detailed, tests. To meet these objectives, a flat plate was mounted on a two-axis traverse in two distinct configurations: (1) as a shield between the jet and the observer and (2) as a reflecting surface on the opposite side of the jet from the observer. The surface length was varied between 2 and 20 jet diameters downstream of the nozzle exit. Similarly, the radial distance from the jet centerline to the surface face was varied between 1 and 16 jet diameters. Far-field and phased array noise data were acquired at each combination of surface length and radial location using two nozzles operating at jet exit conditions across several flow regimes: subsonic cold, subsonic hot, underexpanded, ideally expanded, and overexpanded supersonic. The far-field noise results, discussed here, show where the jet noise is partially shielded by the surface and where jet-surface interaction noise dominates the low frequency spectrum as a surface extends downstream and approaches the jet plume.

scholarly journals Assessment of Linearization Approaches for Multibody Dynamics Formulations

2017 ◽  
Vol 12 (4) ◽  
Author(s):  
Francisco González ◽  
Pierangelo Masarati ◽  
Javier Cuadrado ◽  
Miguel A. Naya
Keyword(s):  
Mechanical System ◽  
Multibody Dynamics ◽  
Equations Of Motion ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Practical Applications ◽  
Linearization Methods ◽  
Highly Nonlinear ◽  
Wide Range ◽  
The Way

Formulating the dynamics equations of a mechanical system following a multibody dynamics approach often leads to a set of highly nonlinear differential-algebraic equations (DAEs). While this form of the equations of motion is suitable for a wide range of practical applications, in some cases it is necessary to have access to the linearized system dynamics. This is the case when stability and modal analyses are to be carried out; the definition of plant and system models for certain control algorithms and state estimators also requires a linear expression of the dynamics. A number of methods for the linearization of multibody dynamics can be found in the literature. They differ in both the approach that they follow to handle the equations of motion and the way in which they deliver their results, which in turn are determined by the selection of the generalized coordinates used to describe the mechanical system. This selection is closely related to the way in which the kinematic constraints of the system are treated. Three major approaches can be distinguished and used to categorize most of the linearization methods published so far. In this work, we demonstrate the properties of each approach in the linearization of systems in static equilibrium, illustrating them with the study of two representative examples.

Calculation of the primary trajectories of seeds and other particles in strong winds

1983 ◽  
Vol 219 (1215) ◽  
pp. 217-217
Keyword(s):  
Equations Of Motion ◽  
Aerodynamic Resistance ◽  
Reynolds Numbers ◽  
Spherical Particles ◽  
Spores And Pollen ◽  
General Terms ◽  
Wide Range ◽  
Strong Winds ◽  
Dispersal Distances ◽  
Enormous Number

The movement of variously dense spherical particles representing a variety of seeds, fruits, spores and pollen, and released from rest into arbitrary winds and a gravitational field is discussed in general terms that account in detail for changes in the quasi-static aerodynamic resistance to motion experienced by such particles during aerial flight. A hybrid analytical-empirical law is established which describes this resistance fairly accurately for particle Reynolds numbers in the range 0—60 000 and that allows for the numerical integration of the equations of motion so as to cover a very wide range of flight conditions. This makes possible the provision of a set of four-parameter universal range tables from which the dispersal distances for an enormous number of practical cases may be estimated. One particular case of particle movement in a region of pseudo-thermal convection is also discussed and this shows how a marked degree of deposition concentration may be induced in some circumstances by such a flow. Botanists and ecologists concerned with seed and particle dispersal in the environment may find the universal range tables of particular interest and use. This is because the tables obviate the need for the integration of the equations of motion when dealing with individual cases and permit an estimation of range purely on the basis of the specified quantities of particle size, density and altitude of release, atmospheric wind speed, density and viscosity, and the acceleration due to gravity.

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