Comparative analysis of the stability of one-dimensional and spherically symmetric solitons of a scalar field with J?J? self-interaction

1980 ◽  
Vol 43 (3) ◽  
pp. 527-532
Author(s):  
I. L. Bogolyubskii
Keyword(s):  
Comparative Analysis ◽  
Scalar Field ◽  
Spherically Symmetric ◽  
One Dimensional ◽  
The Stability

Investigation of two-dimensional nonstationary processes of outflow a gas-saturated liquid from axisymmetric vessels

2012 ◽  
Vol 9 (1) ◽  
pp. 47-52
Author(s):  
R.Kh. Bolotnova ◽  
V.A. Buzina
Keyword(s):  
Comparative Analysis ◽  
Numerical Model ◽  
Liquid Mixture ◽  
Phase Model ◽  
Test Problems ◽  
Two Dimensional ◽  
Nonstationary Processes ◽  
Saturated Liquid ◽  
Two Phase ◽  
One Dimensional

The two-dimensional and two-phase model of the gas-liquid mixture is constructed. The validity of numerical model realization is justified by using a comparative analysis of test problems solution with one-dimensional calculations. The regularities of gas-saturated liquid outflow from axisymmetric vessels for different geometries are established.

scholarly journals On the Numerical Simulation of HPDEs Using θ-Weighted Scheme and the Galerkin Method

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 78
Author(s):  
Haifa Bin Jebreen ◽  
Fairouz Tchier
Keyword(s):  
Differential Equation ◽  
Galerkin Method ◽  
Linear Ordinary Differential Equation ◽  
Time Interval ◽  
Hyperbolic Partial Differential Equation ◽  
Time Step ◽  
Numerical Examples ◽  
One Dimensional ◽  
The Stability ◽  
The Galerkin Method

Herein, an efficient algorithm is proposed to solve a one-dimensional hyperbolic partial differential equation. To reach an approximate solution, we employ the θ-weighted scheme to discretize the time interval into a finite number of time steps. In each step, we have a linear ordinary differential equation. Applying the Galerkin method based on interpolating scaling functions, we can solve this ODE. Therefore, in each time step, the solution can be found as a continuous function. Stability, consistency, and convergence of the proposed method are investigated. Several numerical examples are devoted to show the accuracy and efficiency of the method and guarantee the validity of the stability, consistency, and convergence analysis.

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 Janis–Newman–Winicour and Wyman Solutions are the Same

1997 ◽  
Vol 12 (27) ◽  
pp. 4831-4835 ◽  
Author(s):  
K. S. Virbhadra
Keyword(s):  
Exact Solution ◽  
Scalar Field ◽  
Total Energy ◽  
Space Time ◽  
Massless Scalar ◽  
Spherically Symmetric ◽  
Scalar Equations

We show that the well-known most general static and spherically symmetric exact solution to the Einstein-massless scalar equations given by Wyman is the same as one found by Janis, Newman and Winicour several years ago. We obtain the energy associated with this space–time and find that the total energy for the case of the purely scalar field is zero.

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.

scholarly journals TRAVERSABLE WORMHOLES IN A STRING CLOUD

2008 ◽  
Vol 17 (08) ◽  
pp. 1179-1196 ◽  
Author(s):  
MARTÍN G. RICHARTE ◽  
CLAUDIO SIMEONE
Keyword(s):  
Thin Shell ◽  
Dimensional Space ◽  
Space Time ◽  
Exotic Matter ◽  
Spherically Symmetric ◽  
Related Model ◽  
Traversable Wormholes ◽  
Dimensional Space Time ◽  
Thin Shell Wormholes ◽  
The Stability

We study spherically symmetric thin shell wormholes in a string cloud background in (3 + 1)-dimensional space–time. The amount of exotic matter required for the construction, the traversability and the stability of such wormholes under radial perturbations are analyzed as functions of the parameters of the model. In addition, in the appendices a nonperturbative approach to the dynamics and a possible extension of the analysis to a related model are briefly discussed.

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.

scholarly journals Small-Scale Spectrum of a Scalar Field in Water: The Batchelor and Kraichnan Models

2011 ◽  
Vol 41 (11) ◽  
pp. 2155-2167 ◽  
Author(s):  
Xavier Sanchez ◽  
Elena Roget ◽  
Jesus Planella ◽  
Francesc Forcat
Keyword(s):  
Scalar Field ◽  
Thermal Gradient ◽  
Theoretical Models ◽  
Measured Data ◽  
Small Scale ◽  
Temperature Profiles ◽  
One Dimensional ◽  
Kraichnan Model ◽  
The One ◽  
Rate Of Dissipation

Abstract The theoretical models of Batchelor and Kraichnan, which account for the smallest scales of a scalar field passively advected by a turbulent fluid (Prandtl > 1), have been validated using shear and temperature profiles measured with a microstructure profiler in a lake. The value of the rate of dissipation of turbulent kinetic energy ɛ has been computed by fitting the shear spectra to the Panchev and Kesich theoretical model and the one-dimensional spectra of the temperature gradient, once ɛ is known, to the Batchelor and Kraichnan models and from it determining the value of the turbulent parameter q. The goodness of the fit between the spectra corresponding to these models and the measured data shows a very clear dependence on the degree of isotropy, which is estimated by the Cox number. The Kraichnan model adjusts better to the measured data than the Batchelor model, and the values of the turbulent parameter that better fit the experimental data are qB = 4.4 ± 0.8 and qK = 7.9 ± 2.5 for Batchelor and Kraichnan, respectively, when Cox ≥ 50. Once the turbulent parameter is fixed, a comparison of the value of ɛ determined from fitting the thermal gradient spectra to the value obtained after fitting the shear spectra shows that the Kraichnan model gives a very good estimate of the dissipation, which the Batchelor model underestimates.

FUNCTIONAL INTEGRALS AND PHASE STRUCTURES IN SINE-GORDON–THIRRING MODEL

2012 ◽  
Vol 26 (27) ◽  
pp. 1250178 ◽  
Author(s):  
JUN YAN
Keyword(s):  
Strong Coupling ◽  
Finite Temperature ◽  
Thirring Model ◽  
Attractive Potential ◽  
Functional Integrals ◽  
One Dimensional ◽  
Phase Structures ◽  
Coexistence Phase ◽  
Coupling Case ◽  
The Stability

The phase structures of one-dimensional quantum sine-Gordon–Thirring model with N-impurities coupling are studied in this paper. The effective actions at finite temperature are derived by means of the perturbation and non-perturbation functional integrals method. The stability of coexistence phase is analyzed respectively in the weak and strong coupling case. It is shown that the coexistence phase is not stable when fermions have an attractive potential g < 0, and the stable coexistence phase can form when fermions have an exclude potential g > 0.

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