scholarly journals Dynamics of three dimensional maps

2011 ◽  
Vol 24 (1) ◽  
pp. 105-117
Author(s):  
Asma Djerrai ◽  
Ilhem Djellit
Keyword(s):  
Invariant Manifolds ◽  
Three Dimensional ◽  
One Dimensional ◽  
Research Fields ◽  
Numerical Exploration ◽  
Wide Range ◽  
Planar Maps ◽  
The Stability ◽  
The One ◽  
One Dimensional Maps

Smooth 3D maps have been a focus of study in a wide range of research fields. Their Properties are investigated qualitatively and numerically. These maps show qualitatively interesting types of bifurcations than those exhibited by generic smooth planar maps. We present a theoretical framework for analyzing three-dimensional smooth coupling maps by finding the stability criteria for periodic orbits and characterizing the system behaviors with the tools of nonlinear dynamics relative to bifurcation in the parameter plane, invariant manifolds, critical manifolds, chaotic attractors. We also show by numerical simulation bifurcations that can occur in such maps. By an analytical and numerical exploration we give some properties and characteristics, since this class of three-dimensional dynamics is associated with the properties of one-dimensional maps. There is an interesting passage from the one-dimensional endomorphisms to the three-dimensional endomorphisms.

On the stability of nonlinear waves coexisting with plasma beams

1975 ◽  
Vol 13 (1) ◽  
pp. 173-187 ◽  
Author(s):  
E. Infeld ◽  
G. Rowlands
Keyword(s):  
Nonlinear Wave ◽  
Growth Rates ◽  
Three Dimensional ◽  
Stationary Waves ◽  
One Dimensional ◽  
Long Wavelength ◽  
Long Wave ◽  
Set Up ◽  
The Stability ◽  
The One

In this paper we consider the stability of one-dimensional stationary waves set up by two counter-streaming beams of electrons in a background of stationary ions. The perturbations considered are long-wave in a direction perpendicular to the wave. The presence of a uniform magnetic field in the direction of the wave and the effect of a perpendicular pressure are taken into account. In the long-wavelength limit growth rates are diminished by the nonlinear wave. When the amplitude of this wave tends to its maximum value, the growth rates tend to zero. Thus the wave has a stabilizing effect for long-wave perturbations. Three- dimensional effects lead to additional instabilities which are also quenched by the nonlinear wave, but not as fast as the one-dimensional calculation indicates.

Supramolecular architectures in CoIIand CuIIcomplexes with thiophene-2-carboxylate and 2-amino-4,6-dimethoxypyrimidine ligands

2016 ◽  
Vol 72 (5) ◽  
pp. 442-450 ◽  
Author(s):  
Ammasai Karthikeyan ◽  
Packianathan Thomas Muthiah ◽  
Franc Perdih
Keyword(s):  
Hydrogen Bonds ◽  
Water Molecule ◽  
Coordination Polymers ◽  
Three Dimensional ◽  
Functional Materials ◽  
Supramolecular Architecture ◽  
Dinuclear Copper ◽  
One Dimensional ◽  
Wide Range ◽  
The One

The coordination chemistry of mixed-ligand complexes continues to be an active area of research since these compounds have a wide range of applications. Many coordination polymers and metal–organic framworks are emerging as novel functional materials. Aminopyrimidine and its derivatives are flexible ligands with versatile binding and coordination modes which have been proven to be useful in the construction of organic–inorganic hybrid materials and coordination polymers. Thiophenecarboxylic acid, its derivatives and their complexes exhibit pharmacological properties. Cobalt(II) and copper(II) complexes of thiophenecarboxylate have many biological applications, for example, as antifungal and antitumor agents. Two new cobalt(II) and copper(II) complexes incorporating thiophene-2-carboxylate (2-TPC) and 2-amino-4,6-dimethoxypyrimidine (OMP) ligands have been synthesized and characterized by X-ray diffraction studies, namely (2-amino-4,6-dimethoxypyrimidine-κN)aquachlorido(thiophene-2-carboxylato-κO)cobalt(II) monohydrate, [Co(C5H3O2S)Cl(C6H9N3O2)(H2O)]·H2O, (I), andcatena-poly[copper(II)-tetrakis(μ-thiophene-2-carboxylato-κ2O:O′)-copper(II)-(μ-2-amino-4,6-dimethoxypyrimidine-κ2N1:N3)], [Cu2(C5H3O2S)4(C6H9N3O2)]n, (II). In (I), the CoIIion has a distorted tetrahedral coordination environment involving one O atom from a monodentate 2-TPC ligand, one N atom from an OMP ligand, one chloride ligand and one O atom of a water molecule. An additional water molecule is present in the asymmetric unit. The amino group of the coordinated OMP molecule and the coordinated carboxylate O atom of the 2-TPC ligand form an interligand N—H...O hydrogen bond, generating anS(6) ring motif. The pyrimidine molecules also form a base pair [R22(8) motif]viaa pair of N—H...N hydrogen bonds. These interactions, together with O—H...O and O—H...Cl hydrogen bonds and π–π stacking interactions, generate a three-dimensional supramolecular architecture. The one-dimensional coordination polymer (II) contains the classical paddle-wheel [Cu2(CH3COO)4(H2O)2] unit, where each carboxylate group of four 2-TPC ligands bridges two square-pyramidally coordinated CuIIions and the apically coordinated OMP ligands bridge the dinuclear copper units. Each dinuclear copper unit has a crystallographic inversion centre, whereas the bridging OMP ligand has crystallographic twofold symmetry. The one-dimensional polymeric chains self-assembleviaN—H...O, π–π and C—H...π interactions, generating a three-dimensional supramolecular architecture.

BORDER COLLISION BIFURCATIONS IN THREE-DIMENSIONAL PIECEWISE SMOOTH SYSTEMS

2008 ◽  
Vol 18 (02) ◽  
pp. 577-586 ◽  
Author(s):  
INDRAVA ROY ◽  
A. R. ROY
Keyword(s):  
Three Dimensional ◽  
Piecewise Smooth ◽  
Smooth Maps ◽  
Research Fields ◽  
Border Collision Bifurcations ◽  
Period 2 ◽  
Wide Range ◽  
Different Types ◽  
Piecewise Smooth Maps ◽  
The Stability

Piecewise smooth maps have been a focus of study for scientists in a wide range of research fields. These maps show qualitatively different types of bifurcations than those exhibited by generic smooth maps. We present a theoretical framework for analyzing three-dimensional piecewise smooth maps by deriving a suitable normal form and then finding the stability criteria for periodic orbits. We also show by numerical simulation different types of border collision bifurcations that can occur in such a map. We have also been able to observe a border collision bifurcation from a period-2 to a quasiperiodic orbit.

scholarly journals EXTENDING A HYBRID GODUNOV METHOD FOR RADIATION HYDRODYNAMICS TO MULTIPLE DIMENSIONS

2011 ◽  
Vol 22 (05) ◽  
pp. 457-481
Author(s):  
MICHAEL D. SEKORA
Keyword(s):  
Three Dimensional ◽  
Godunov Method ◽  
Computational Technique ◽  
Radiation Hydrodynamics ◽  
One Dimensional ◽  
Numerical Tests ◽  
Future Paper ◽  
Multiple Dimensions ◽  
Wide Range ◽  
The One

This paper presents a hybrid Godunov method for three-dimensional radiation hydrodynamics. The multidimensional technique outlined in this paper is an extension of the one-dimensional method that was developed by Sekora and Stone 2009, 2010. The earlier one-dimensional technique was shown to preserve certain asymptotic limits and be uniformly well behaved from the photon free streaming (hyperbolic) limit through the weak equilibrium diffusion (parabolic) limit and to the strong equilibrium diffusion (hyperbolic) limit. This paper gives the algorithmic details for constructing a multidimensional method. A future paper will present numerical tests that demonstrate the robustness of the computational technique across a wide-range of parameter space.

Exploring the Multidimensional Facets of Authoritarianism: Authoritarian Aggression and Social Dominance Orientation

2008 ◽  
Vol 67 (1) ◽  
pp. 51-60 ◽  
Author(s):  
Stefano Passini
Keyword(s):  
Social Dominance ◽  
Factor Model ◽  
Three Dimensional ◽  
Social Dominance Orientation ◽  
Model Fit ◽  
Regression Analyses ◽  
One Dimensional ◽  
Confirmatory Factor ◽  
The One ◽  
Better Than

The relation between authoritarianism and social dominance orientation was analyzed, with authoritarianism measured using a three-dimensional scale. The implicit multidimensional structure (authoritarian submission, conventionalism, authoritarian aggression) of Altemeyer’s (1981, 1988) conceptualization of authoritarianism is inconsistent with its one-dimensional methodological operationalization. The dimensionality of authoritarianism was investigated using confirmatory factor analysis in a sample of 713 university students. As hypothesized, the three-factor model fit the data significantly better than the one-factor model. Regression analyses revealed that only authoritarian aggression was related to social dominance orientation. That is, only intolerance of deviance was related to high social dominance, whereas submissiveness was not.

scholarly journals Stability of a one-dimensional morphoelastic model for post-burn contraction

2021 ◽  
Vol 83 (3) ◽  
Author(s):  
Ginger Egberts ◽  
Fred Vermolen ◽  
Paul van Zuijlen
Keyword(s):  
Wound Healing ◽  
Residual Stresses ◽  
Truncation Error ◽  
Signaling Molecules ◽  
Discrete Problem ◽  
One Dimensional ◽  
Stability Constraint ◽  
Biological Interpretation ◽  
The Stability ◽  
The One

AbstractTo deal with permanent deformations and residual stresses, we consider a morphoelastic model for the scar formation as the result of wound healing after a skin trauma. Next to the mechanical components such as strain and displacements, the model accounts for biological constituents such as the concentration of signaling molecules, the cellular densities of fibroblasts and myofibroblasts, and the density of collagen. Here we present stability constraints for the one-dimensional counterpart of this morphoelastic model, for both the continuous and (semi-) discrete problem. We show that the truncation error between these eigenvalues associated with the continuous and semi-discrete problem is of order $${{\mathcal {O}}}(h^2)$$ O ( h 2 ) . Next we perform numerical validation to these constraints and provide a biological interpretation of the (in)stability. For the mechanical part of the model, the results show the components reach equilibria in a (non) monotonic way, depending on the value of the viscosity. The results show that the parameters of the chemical part of the model need to meet the stability constraint, depending on the decay rate of the signaling molecules, to avoid unrealistic results.

scholarly journals One-Dimensional Organic–Inorganic Material (C6H9N2)2BiCl5: From Synthesis to Structural, Spectroscopic, and Electronic Characterizations

2021 ◽  
Vol 22 (4) ◽  
pp. 2030
Author(s):  
Hela Ferjani ◽  
Hammouda Chebbi ◽  
Mohammed Fettouhi
Keyword(s):  
Hydrogen Bonding ◽  
Density Functional ◽  
Crystal Packing ◽  
Diffuse Reflectance Spectrum ◽  
Enrichment Ratio ◽  
One Dimensional ◽  
Organic Part ◽  
Fukui Indices ◽  
The Stability ◽  
The One

The new organic–inorganic compound (C6H9N2)2BiCl5 (I) has been grown by the solvent evaporation method. The one-dimensional (1D) structure of the allylimidazolium chlorobismuthate (I) has been determined by single crystal X-ray diffraction. It crystallizes in the centrosymmetric space group C2/c and consists of 1-allylimidazolium cations and (1D) chains of the anion BiCl52−, built up of corner-sharing [BiCl63−] octahedra which are interconnected by means of hydrogen bonding contacts N/C–H⋯Cl. The intermolecular interactions were quantified using Hirshfeld surface analysis and the enrichment ratio established that the most important role in the stability of the crystal structure was provided by hydrogen bonding and H···H interactions. The highest value of E was calculated for the contact N⋯C (6.87) followed by C⋯C (2.85) and Bi⋯Cl (2.43). These contacts were favored and made the main contribution to the crystal packing. The vibrational modes were identified and assigned by infrared and Raman spectroscopy. The optical band gap (Eg = 3.26 eV) was calculated from the diffuse reflectance spectrum and showed that we can consider the material as a semiconductor. The density functional theory (DFT) has been used to determine the calculated gap, which was about 3.73 eV, and to explain the electronic structure of the title compound, its optical properties, and the stability of the organic part by the calculation of HOMO and LUMO energy and the Fukui indices.

A TWELFTH-ORDER FOUR-STEP FORMULA FOR THE NUMERICAL INTEGRATION OF THE ONE-DIMENSIONAL SCHRÖDINGER EQUATION

2003 ◽  
Vol 14 (08) ◽  
pp. 1087-1105 ◽  
Author(s):  
ZHONGCHENG WANG ◽  
YONGMING DAI
Keyword(s):  
Schrödinger Equation ◽  
Numerical Integration ◽  
Schrodinger Equation ◽  
Numerical Test ◽  
New Method ◽  
Step Method ◽  
One Dimensional ◽  
The Stability ◽  
The One ◽  
Order Four

A new twelfth-order four-step formula containing fourth derivatives for the numerical integration of the one-dimensional Schrödinger equation has been developed. It was found that by adding multi-derivative terms, the stability of a linear multi-step method can be improved and the interval of periodicity of this new method is larger than that of the Numerov's method. The numerical test shows that the new method is superior to the previous lower orders in both accuracy and efficiency and it is specially applied to the problem when an increasing accuracy is requested.

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