THE 2-D SEXTIC HAMILTONIAN OSCILLATOR

2013 ◽  
Vol 23 (06) ◽  
pp. 1330019
Author(s):  
F. J. MOLERO ◽  
J. C. VAN DER MEER ◽  
S. FERRER ◽  
F. J. CÉSPEDES
Keyword(s):  
Phase Space ◽  
Elliptic Functions ◽  
Singular Values ◽  
Nonlinear Oscillators ◽  
Momentum Mapping ◽  
Dimensional Model ◽  
Integrable Hamiltonian Systems ◽  
One Dimensional ◽  
Dimensional Phase Space ◽  
The One

The 2-D sextic oscillator is studied as a family of axial symmetric parametric integrable Hamiltonian systems, presenting a bifurcation analysis of the different flows. It includes the "elliptic core" model in 1-D nonlinear oscillators, recently proposed in the literature. We make use of the energy-momentum mapping, which will give us the fundamental fibration of the four-dimensional phase space. Special attention is given to the singular values of the energy-momentum mapping connected with rectilinear and circular orbits. They are related to the saddle-center and pitchfork scenarios with the associated homoclinic and heteroclinic trajectories. We also study how the geometry of the phase space evolves during the transition from the one-dimensional to the two-dimensional model. Within an elliptic function approach, the solutions are given using Legendre elliptic integrals of the first and third kind and the corresponding Jacobi elliptic functions.

MECHANICAL STICK-SLIP VIBRATIONS

1995 ◽  
Vol 05 (03) ◽  
pp. 637-651 ◽  
Author(s):  
U. GALVANETTO ◽  
S.R. BISHOP ◽  
L. BRISEGHELLA
Keyword(s):  
Phase Space ◽  
Three Dimensional ◽  
Basins Of Attraction ◽  
Global Dynamics ◽  
Chaotic Oscillations ◽  
Stick Slip ◽  
One Dimensional ◽  
Dimensional Phase Space ◽  
The One ◽  
Two Degree Of Freedom

In this paper we consider the behavior of a two degree-of-freedom mechanical system incorporating static and dynamic friction, assumed to be a decreasing function of the relative sliding velocity. The model consists of two blocks linked by springs, which ride upon a moving belt. The dynamics of the system are described within a four-dimensional phase space. A three-dimensional Poincaré map is discussed together with a simpler one-dimensional map of a scalar variable. Considering the one-dimensional map it is possible to study all the attractors of the system for small belt velocities including the construction of one-dimensional basins of attraction. Thus, albeit in a partial zone of the control-phase space, the global dynamics of the system can be characterized displaying periodic, quasi-periodic and chaotic oscillations.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

Modelling Techniques in Applied Glaciology: Numerical Modelling of Avalanches

1983 ◽  
Vol 4 ◽  
pp. 297-297
Author(s):  
G. Brugnot
Keyword(s):  
Finite Difference Method ◽  
Transverse Velocity ◽  
Longitudinal Velocity ◽  
Momentum Conservation ◽  
Dimensional Model ◽  
One Dimensional ◽  
Modelling Techniques ◽  
Reference Grid ◽  
The One ◽  
Near Future

We consider the paper by Brugnot and Pochat (1981), which describes a one-dimensional model applied to a snow avalanche. The main advance made here is the introduction of the second dimension in the runout zone. Indeed, in the channelled course, we still use the one-dimensional model, but, when the avalanche spreads before stopping, we apply a (x, y) grid on the ground and six equations have to be solved: (1) for the avalanche body, one equation for continuity and two equations for momentum conservation, and (2) at the front, one equation for continuity and two equations for momentum conservation. We suppose the front to be a mobile jump, with longitudinal velocity varying more rapidly than transverse velocity.We solve these equations by a finite difference method. This involves many topological problems, due to the actual position of the front, which is defined by its intersection with the reference grid (SI, YJ). In the near future our two directions of research will be testing the code on actual avalanches and improving it by trying to make it cheaper without impairing its accuracy.

scholarly journals Order parameter profiles in a system with Neumann – Neumann boundary conditions

2018 ◽  
Vol 145 ◽  
pp. 01009 ◽  
Author(s):  
Vassil M. Vassilev ◽  
Daniel M. Dantchev ◽  
Peter A. Djondjorov
Keyword(s):  
Boundary Conditions ◽  
Order Parameter ◽  
Neumann Boundary ◽  
Elliptic Functions ◽  
Thermodynamic System ◽  
Neumann Boundary Conditions ◽  
Ginzburg Landau ◽  
One Dimensional ◽  
The One ◽  
Field Plane

In this article we consider a critical thermodynamic system with the shape of a thin film confined between two parallel planes. It is assumed that the state of the system at a given temperature and external ordering field is described by order-parameter profiles, which minimize the one-dimensional counterpart of the standard ϕ4 Ginzburg–Landau Hamiltonian and meet the so-called Neumann – Neumann boundary conditions. We give analytic representation of the extremals of this variational problem in terms ofWeierstrass elliptic functions. Then, depending on the temperature and ordering field we determine the minimizers and obtain the phase diagram in the temperature-field plane.

A Stefan problem in a Bridgman crystal grower

1995 ◽  
Vol 6 (3) ◽  
pp. 191-199
Author(s):  
P. den Decker ◽  
R. van der Hout ◽  
C. J. Van Duijn ◽  
L. A. Peletier
Keyword(s):  
Critical Speed ◽  
Internal Heat ◽  
Mushy Region ◽  
Dimensional Model ◽  
Real Situation ◽  
One Dimensional ◽  
Dimensional Approximation ◽  
The One ◽  
Strong Curvature ◽  
Bridgman Crystal Grower

We discuss a one-dimensional model for a Bridgman crystal grower, where the removal of heat is described by an internal heat sink. A consequence is the apparent existence of mushy regions for relatively large velocities of the cooling machine; these mushy regions are an artefact of the one-dimensional approximation. We show that for some types of cooling profiles there exists a critical speed for the existence of mushy regions, whereas for different cooling profiles no such critical speed exists. The presence of a mushy region may indicate a strong curvature of the liquid/solid interface in the real situation.

On the numerical study of thermohydrodynamics and biochemistry of inland water bodies

2021 ◽  
Author(s):  
Daria Gladskikh ◽  
Evgeny Mortikov ◽  
Victor Stepanenko
Keyword(s):  
Mixed Layer ◽  
Numerical Study ◽  
Three Dimensional ◽  
Water Bodies ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
One Dimensional ◽  
Lake Model ◽  
Upper Mixed Layer ◽  
The One

<p>The study of thermodynamic and biochemical processes of inland water objects using one- and three-dimensional RANS numerical models was carried out both for idealized water bodies and using measurements data. The need to take into account seiche oscillations to correctly reproduce the deepening of the upper mixed layer in one-dimensional (vertical) models is demonstrated. We considered the one-dimensional LAKE model [1] and the three-dimensional model [2, 3, 4] developed at the Research Computing Center of Moscow State University on the basis of a hydrodynamic code combining DNS/LES/RANS approaches for calculating geophysical turbulent flows. The three-dimensional model was supplemented by the equations for calculating biochemical substances by analogy with the one-dimensional biochemistry equations used in the LAKE model. The effect of mixing processes on the distribution of concentration of greenhouse gases, in particular, methane and oxygen, was studied.</p><p>The work was supported by grants of the RF President’s Grant for Young Scientists (MK-1867.2020.5, MD-1850.2020.5) and by the RFBR (19-05-00249, 20-05-00776). </p><p>1. Stepanenko V., Mammarella I., Ojala A., Miettinen H., Lykosov V., Timo V. LAKE 2.0: a model for temperature, methane, carbon dioxide and oxygen dynamics in lakes // Geoscientific Model Development. 2016. V. 9(5). P. 1977–2006.<br>2. Mortikov E.V., Glazunov A.V., Lykosov V.N. Numerical study of plane Couette flow: turbulence statistics and the structure of pressure-strain correlations // Russian Journal of Numerical Analysis and Mathematical Modelling. 2019. 34(2). P. 119-132.<br>3. Mortikov, E.V. Numerical simulation of the motion of an ice keel in stratified flow // Izv. Atmos. Ocean. Phys. 2016. V. 52. P. 108-115.<br>4. Gladskikh D.S., Stepanenko V.M., Mortikov E.V. On the influence of the horizontal dimensions of inland waters on the thickness of the upper mixed layer // Water Resourses. 2021.V. 45, 9 pages. (in press) </p>

scholarly journals Hydraulic modeling of combined sewers overflow integrating the results of the SWMM and CFX models.

2021 ◽  
Vol 37 (1) ◽  
Author(s):  
D. Pulgarín ◽  
J. Plaza ◽  
J. Ruge ◽  
J. Rojas
Keyword(s):  
Three Dimensional ◽  
Hydraulic Modeling ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
One Dimensional ◽  
Ansys Cfx ◽  
Combined Sewer ◽  
The One ◽  
Swmm Model

This study proposes a methodology for the calibration of combined sewer overflow (CSO), incorporating the results of the three-dimensional ANSYS CFX model in the SWMM one-dimensional model. The procedure consists of constructing calibration curves in ANSYS CFX that relate the input flow to the CSO with the overflow, to then incorporate them into the SWMM model. The results obtained show that the behavior of the flow over the crest of the overflow weir varies in space and time. Therefore, the flow of entry to the CSO and the flow of excesses maintain a non-linear relationship, contrary to the results obtained in the one-dimensional model. However, the uncertainty associated with the idealization of flow methodologies in one dimension is reduced under the SWMM model with kinematic wave conditions and simulating CSO from curves obtained in ANSYS CFX. The result obtained facilitates the calibration of combined sewer networks for permanent or non-permanent flow conditions, by means of the construction of curves in a three-dimensional model, especially when the information collected in situ is limited.

One-Dimensional Harmonic Oscillator in Quantum Phase Space

2011 ◽  
Vol 110-116 ◽  
pp. 3750-3754
Author(s):  
Jun Lu ◽  
Xue Mei Wang ◽  
Ping Wu
Keyword(s):  
Phase Space ◽  
Harmonic Oscillator ◽  
Quantum Phase ◽  
Space Representation ◽  
Wave Mechanics ◽  
One Dimensional ◽  
Matrix Mechanics ◽  
The Matrix ◽  
Quantum Wave ◽  
The One

Within the framework of the quantum phase space representation established by Torres-Vega and Frederick, we solve the rigorous solutions of the stationary Schrödinger equations for the one-dimensional harmonic oscillator by means of the quantum wave-mechanics method. The result shows that the wave mechanics and the matrix mechanics are equivalent in phase space, just as in position or momentum space.

Quantum entanglement in some topological insulator models

2019 ◽  
Vol 33 (24) ◽  
pp. 1950284 ◽  
Author(s):  
L. S. Lima
Keyword(s):  
Quantum Entanglement ◽  
Topological Insulator ◽  
Topological Charge ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Model Case ◽  
Topological Transition ◽  
One Dimensional ◽  
Zhang Model ◽  
The One

Quantum entanglement is studied in the neighborhood of a topological transition in some topological insulator models such as the two-dimensional Qi–Wu–Zhang model or Chern insulator. The system describes electrons hopping in two-dimensional chains. For the one-dimensional model case, there exist staggered hopping amplitudes. Our results show a strong effect of sudden variation of the topological charge Q in the neighborhood of phase transition on quantum entanglement for all the cases analyzed.

scholarly journals Quantitative Spectroscopy of Wolf-Rayet Stars

1988 ◽  
Vol 108 ◽  
pp. 133-140
Author(s):  
W. Schmutz
Keyword(s):  
Representative Point ◽  
Dimensional Model ◽  
Model Calculations ◽  
One Dimensional ◽  
The Past ◽  
First Results ◽  
The One ◽  
Expanding Atmospheres ◽  
New Generation ◽  
The Continuum

Advances in theoretical modeling of rapidly expanding atmospheres in the past few years made it possible to determine the stellar parameters of the Wolf-Rayet stars. This progress is mainly due to the improvement of the models with respect to their spatial extension: The new generation of models treat spherically-symmetric expanding atmospheres, i.e. the models are one-dimensional. Older models describe the wind by only one representative point. The older models are in fact ‘core-halo’ approximations. They have been introduced by Castor and van Blerkom (1970), and were extensively employed in the past (cf. e.g. Willis and Wilson, 1978; Smith and Willis, 1982). First results from new one-dimensional model calculations are published by Hillier (1984), Schmutz (1984), Hamann (1985), Hillier (1986), and Schmutz et al. (1987a); more detailed results are presented by Schmutz and Hamann (1986), Hamann and Schmutz (1987), Hillier (1987a,b), Wessolowski et al. (1987), Hillier (1987c) and Hamann et al. (1987). These results demonstrate that the step from zero- to one-dimensional calculations is essential. The important point is that the complicated interrelation between NLTE-level populations and radiation field is treated adequately (Schmutz and Hamann, 1986; Hillier, 1987). For this interrelation it is crucial to model consistently not only the line-formation region, but also the layers where the continuum is emitted. In fact, it is the core-halo approximation that causes the one-point models to fail in certain aspects.

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