Relaxation times obtained from the rate equations using path probability method for the spin-1 Ising model

2019 ◽  
Vol 33 (22) ◽  
pp. 1950258 ◽  
Author(s):  
Rıza Erdem ◽  
Songül Özüm
Keyword(s):  
Ising Model ◽  
Relaxation Times ◽  
Phenomenological Theory ◽  
Equilibrium States ◽  
Time Dependent ◽  
Rate Equations ◽  
Probability Method ◽  
Temperature Variations ◽  
Path Probability Method ◽  
Good Agreement

We have presented the time-dependent behaviors of a spin-1 Ising model (with both bilinear and biquadratic interactions) in the neighborhood of the equilibrium states via the path probability method. The rate equations as introduced by Keskin and co-workers (1989) have been linearized to obtain the characteristic relaxation times. The temperature variations of these times were produced in accordance with the Tanaka and Mannari’s work (1976) on the equilibrium properties. Results are compared to one using Onsager’s phenomenological theory and a good agreement is achieved.

Determination of the steady-state kinetics in a spin-1 Ising model using path probability method

2020 ◽  
Vol 34 (30) ◽  
pp. 2050338 ◽  
Author(s):  
Songül Özüm ◽  
Rıza Erdem
Keyword(s):  
Steady State ◽  
Ising Model ◽  
Linear Equations ◽  
Kinetic Equations ◽  
Phenomenological Approach ◽  
Rate Equations ◽  
Probability Method ◽  
Steady State Kinetics ◽  
Path Probability Method

As a continuation of our previously published work, we propose a theoretical framework for the determination of steady-state kinetics in a spin-1 Ising model by the path probability method. The framework is based on the principles of non-equilibrium statistical physics and is quite different from the phenomenological approach. We construct a set of linear kinetic equations for the order parameters using the non-linear dynamic (or rate) equations in the presence of external magnetic field. From the steady-state solutions of the linear equations, an expression for the complex (or dynamic) magnetic susceptibility [Formula: see text] is derived. The temperature dependence of the magnetic dispersion relation [Formula: see text] and magnetic absorption factor [Formula: see text] has been studied in the ferromagnetic (FM) and paramagnetic (PM) phases as well as near the critical regime.

Time-dependent numerical modelling of hydroxyl masers

2017 ◽  
Vol 13 (S336) ◽  
pp. 59-60
Author(s):  
J. P. Maswanganye ◽  
D. J. van der Walt ◽  
S. Goedhart
Keyword(s):  
Numerical Modelling ◽  
Temperature Variation ◽  
Time Dependent ◽  
Rate Equations ◽  
Temperature Variations ◽  
Dust Temperature ◽  
One To One ◽  
Hydroxyl Masers

AbstractThe statistical rate equations are used to model the OH masers to see if they will always have a one-to-one correspondence with the variation of dust temperature. It is concluded that one has to be careful to argue that the masers will always follow the dust temperature variation profile, and it is possible that different maser transitions from the same molecule respond differently to the same dust temperature variations.

scholarly journals ANALYSIS OF TIME-EIGENVALUE AND EIGENFUNCTIONS IN THE CROCUS BENCHMARK

2021 ◽  
Vol 247 ◽  
pp. 04011
Author(s):  
Yasushi Nauchi ◽  
Alexis Jinaphanh ◽  
Andrea Zoia
Keyword(s):  
Neutron Emission ◽  
Neutron Transport ◽  
Fission Neutron ◽  
Time Dependent ◽  
Natural Mode ◽  
Probability Method ◽  
Dominant Eigenvalue ◽  
Transport Calculation ◽  
Fission Probability ◽  
Good Agreement

Time-dependent neutron transport in non-critical state can be expressed by the natural mode equation. In order to estimate the dominant eigenvalue and eigenfunction of the natural mode, CEA had extended the α-k method and developed the generalized iterated fission probability method (G-IFP) in the TRIPOLI-4® code. CRIEPI has chosen to compute those quantities by a time-dependent neutron transport calculation, and has thus developed a time-dependent neutron transport technique based on k-power iteration (TDPI) in MCNP-5. In this work, we compare the two approaches by computing the dominant eigenvalue and the direct and adjoint eigenfunctions for the CROCUS benchmark. The model has previously been qualified for keffs and kinetic parameters by TRIPOLI-4 and MCNP-5. The eigenvalues of the natural mode equations by α-k and TDPI are in good agreement with each other, and closely follow those predicted by the inhour equation. Neutron spectra and spatial distributions (flux and fission neutron emission) obtained by the two methods are also in good agreement. Similar results are also obtained for the adjoint fundamental eigenfunctions. These findings substantiate the coherence of both calculation strategies for natural mode.

scholarly journals The Carnot Cycle, Reversibility and Entropy

Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 810
Author(s):  
David Sands
Keyword(s):  
Irreversible Process ◽  
Entropy Change ◽  
External Pressure ◽  
Step Change ◽  
Equilibrium States ◽  
Rate Equations ◽  
Carnot Cycle ◽  
Work Processes ◽  
Reversible Process ◽  
External Conditions

The Carnot cycle and the attendant notions of reversibility and entropy are examined. It is shown how the modern view of these concepts still corresponds to the ideas Clausius laid down in the nineteenth century. As such, they reflect the outmoded idea, current at the time, that heat is motion. It is shown how this view of heat led Clausius to develop the entropy of a body based on the work that could be performed in a reversible process rather than the work that is actually performed in an irreversible process. In consequence, Clausius built into entropy a conflict with energy conservation, which is concerned with actual changes in energy. In this paper, reversibility and irreversibility are investigated by means of a macroscopic formulation of internal mechanisms of damping based on rate equations for the distribution of energy within a gas. It is shown that work processes involving a step change in external pressure, however small, are intrinsically irreversible. However, under idealised conditions of zero damping the gas inside a piston expands and traces out a trajectory through the space of equilibrium states. Therefore, the entropy change due to heat flow from the reservoir matches the entropy change of the equilibrium states. This trajectory can be traced out in reverse as the piston reverses direction, but if the external conditions are adjusted appropriately, the gas can be made to trace out a Carnot cycle in P-V space. The cycle is dynamic as opposed to quasi-static as the piston has kinetic energy equal in difference to the work performed internally and externally.

scholarly journals Rate Equation Modelling of Nonlinear Dynamics in Directly Modulated Multiple Quantum Well Laser Diodes

VLSI Design ◽  
1998 ◽  
Vol 8 (1-4) ◽  
pp. 355-360 ◽  
Author(s):  
Stephen Bennett ◽  
Christopher M. Snowden ◽  
Stavros Iezekiel
Keyword(s):  
Nonlinear Dynamics ◽  
Quantum Well ◽  
Multiple Quantum Well ◽  
Period Doubling ◽  
Rate Equations ◽  
Multiple Quantum ◽  
Quantum Well Laser ◽  
Wide Range ◽  
Multiple Quantum Well Laser ◽  
Good Agreement

A theoretical (using rate equations) and experimental study of the nonlinear dynamics of a distributed feedback multiple quantum well laser diode is presented. The analysis is performed under direct modulation. Period doubling and period tripling are identified in both the measurements and simulations. Period doubling is found over a wide range of modulation frequencies in the laser. Computational results using rate equations show good agreement with the experimental results.

scholarly journals CORRECTION OF POLYRIBOSOME DISTRIBUTIONS AS OBSERVED IN CELL SECTIONS BY ELECTRON MICROSCOPY

1964 ◽  
Vol 22 (3) ◽  
pp. 613-621 ◽  
Author(s):  
William Perl
Keyword(s):  
Electron Microscopy ◽  
Probability Method ◽  
Section Thickness ◽  
Thin Sections ◽  
Comparison Of The Results ◽  
Good Agreement ◽  
Rabbit Reticulocytes

Clusters of ribosomes observed by electron microscopy in thin sections of rabbit reticulocytes are of the same order of size as the section thickness of 600 A. Many of the observed clusters must therefore have been transected by the section surfaces and observed as clusters containing fewer ribosomes. A probability method of correcting for this effect is given. Comparison of the results with grid observations of ribosome distributions indicates sufficiently good agreement for application to cell section observations.

Sign in / Sign up

Export Citation Format

Share Document