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.

scholarly journals Nonlinear Dynamics of a Periodically Driven Duffing Resonator Coupled to a Van der Pol Oscillator

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
X. Wei ◽  
M. F. Randrianandrasana ◽  
M. Ward ◽  
D. Lowe
Keyword(s):  
Strong Coupling ◽  
Internal Resonance ◽  
Weak Coupling ◽  
Response Pattern ◽  
Coupled System ◽  
Van Der Pol Oscillator ◽  
Van Der Pol ◽  
Periodically Driven ◽  
Coupling Case ◽  
The Stability

We explore the dynamics of a periodically driven Duffing resonator coupled elastically to a van der Pol oscillator in the case of 1 : 1 internal resonance in the cases of weak and strong coupling. Whilst strong coupling leads to dominating synchronization, the weak coupling case leads to a multitude of complex behaviours. A two-time scales method is used to obtain the frequency-amplitude modulation. The internal resonance leads to an antiresonance response of the Duffing resonator and a stagnant response (a small shoulder in the curve) of the van der Pol oscillator. The stability of the dynamic motions is also analyzed. The coupled system shows a hysteretic response pattern and symmetry-breaking facets. Chaotic behaviour of the coupled system is also observed and the dependence of the system dynamics on the parameters are also studied using bifurcation analysis.

CRITICAL SCALING BEHAVIOR IN COUPLED MAGNETIC OSCILLATORS

1999 ◽  
Vol 13 (18) ◽  
pp. 2405-2429
Author(s):  
SANG-YOON KIM
Keyword(s):  
Critical Line ◽  
Stability Diagram ◽  
Critical Scaling ◽  
Critical Set ◽  
One Dimensional ◽  
Coupling Case ◽  
Global Coupling ◽  
The Stability ◽  
One Dimensional Maps ◽  
Zero Coupling

We study the critical scaling behaviors of period doublings in N (N=2,3,4,…) coupled magnetic oscillators by varying the driving amplitude A and the coupling strength c. It is found that the critical scaling behaviors depend on the range of coupling. For the extreme long-range case of global coupling, the critical set (set of critical points) is composed of the zero-coupling critical point with c=0 and an infinity of critical line segments in the A-c plane, independently of N. Three kinds of critical scaling behaviors are found on the critical set. However, for any other nonglobal-coupling cases of shorter-range couplings, the structure of the critical set becomes different from that for the global-coupling case, because of a significant change in the stability diagram. We also note that the structure of the critical set and the critical scaling behaviors for both cases of the global and nonglobal couplings are the same as those in the abstract system of the coupled one-dimensional maps.

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 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.

Static Freezing Transition at a Finite Temperature in a Quasi-One-Dimensional Deuteron Glass

1996 ◽  
Vol 76 (13) ◽  
pp. 2330-2333 ◽  
Author(s):  
J. Hemberger ◽  
H. Ries ◽  
A. Loidl ◽  
R. Böhmer
Keyword(s):  
Finite Temperature ◽  
Freezing Transition ◽  
One Dimensional

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 Finite-temperature effects on interacting bosonic one-dimensional systems in disordered lattices

2016 ◽  
Vol 93 (3) ◽  
Author(s):  
Lorenzo Gori ◽  
Thomas Barthel ◽  
Avinash Kumar ◽  
Eleonora Lucioni ◽  
Luca Tanzi ◽  
...  
Keyword(s):  
Finite Temperature ◽  
Temperature Effects ◽  
One Dimensional
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