Modeling the spread of an epidemic in presence of vaccination using cellular automata

2022 ◽  
Author(s):  
Agniva Datta ◽  
Muktish Acharyya
Keyword(s):  
Cellular Automata ◽  
Lattice Model ◽  
Present Model ◽  
Mean Field ◽  
Sir Model ◽  
Linear Behavior ◽  
Basic Goal ◽  
Ca Model ◽  
The Mean ◽  
Good Agreement

The results of Kermack–McKendrick SIR model are planned to be reproduced by cellular automata (CA) lattice model. The CA algorithms are proposed to study the model of an epidemic, systematically. The basic goal is to capture the effects of spreading of infection over a scale of length. This CA model can provide the rate of growth of the infection over the space which was lacking in the mean-field like susceptible-infected-removed (SIR) model. The motion of the circular front of an infected cluster shows a linear behavior in time. The correlation of a particular site to be infected with respect to the central site is also studied. The outcomes of the CA model are in good agreement with those obtained from SIR model. The results of vaccination have been also incorporated in the CA algorithm with a satisfactory degree of success. The advantage of the present model is that it can shed a considerable amount of light on the physical properties of the spread of a typical epidemic in a simple, yet robust way.

New statistical lattice model with double honeycomb symmetry

2014 ◽  
Vol 28 (15) ◽  
pp. 1450086 ◽  
Author(s):  
S. Naji ◽  
A. Belhaj ◽  
H. Labrim ◽  
M. Bhihi ◽  
A. Benyoussef ◽  
...  
Keyword(s):  
Ground State ◽  
Lattice Model ◽  
Present Model ◽  
Hexagonal Lattice ◽  
Mean Field ◽  
Field Approximation ◽  
Hexagonal Structure ◽  
Mean Field Approximation ◽  
Two Dimensional Materials ◽  
The Mean

Inspired from the connection between Lie symmetries and two-dimensional materials, we propose a new statistical lattice model based on a double hexagonal structure appearing in the G2 symmetry. We first construct an Ising-1/2 model, with spin values σ = ±1, exhibiting such a symmetry. The corresponding ground state shows the ferromagnetic, the antiferromagnetic, the partial ferrimagnetic and the topological ferrimagnetic phases depending on the exchange couplings. Then, we examine the phase diagrams and the magnetization using the mean field approximation (MFA). Among others, it has been suggested that the present model could be localized between systems involving the triangular and the single hexagonal lattice geometries.

scholarly journals Magnetocaloric Effect in Nanosystems Based on Ferromagnets with Different Curie Temperatures

2021 ◽  
Vol 132 (1) ◽  
pp. 79-93
Author(s):  
M. A. Kuznetsov ◽  
A. B. Drovosekov ◽  
A. A. Fraerman
Keyword(s):  
Field Theory ◽  
Magnetocaloric Effect ◽  
Landau Theory ◽  
Mean Field Theory ◽  
Mean Field ◽  
Maxwell Relation ◽  
Magnetic Cooling ◽  
The Mean ◽  
Curie Temperatures ◽  
Good Agreement

Abstract The magnetocaloric effect in nanosystems based on exchange-coupled ferromagnets with different Curie temperatures is calculated within the mean-field theory. Good agreement between the results of the mean-field theory and the Landau theory, valid near the critical phase transition temperature, is demonstrated for a flat-layered Fe/Gd/Fe structure. We show that a high magnetic cooling efficiency in this system is attainable in principle and prove the validity of the Maxwell relation, enabling an experimental verification of the predictions made. The theory developed for flat-layered structures is generalized to a granular medium.

A thermodynamic model of hemoglobin suitable for physiological applications

1990 ◽  
Vol 258 (3) ◽  
pp. C563-C577 ◽  
Author(s):  
T. Yoshida ◽  
M. Dembo
Keyword(s):  
Binding Sites ◽  
Electrostatic Interactions ◽  
Mean Field ◽  
Quantitative Model ◽  
Confidence Limits ◽  
Efficient Computation ◽  
Ligand Binding Sites ◽  
The Mean ◽  
Field Formalism ◽  
Good Agreement

We propose a quantitative model of the thermodynamics of hemoglobin in contact with its five major ligands (O2, CO2, Cl-, 2,3-bisphosphoglycerate, and H+). Our model incorporates the two-state formalism of J. Monod, J. Wyman, and J.P. Changeux (J. Mol. Biol. 12: 88-118, 1965) for treatment of quanternary transitions and also the mean field formalism of K. Linderstrom-Lang (C. R. Trav. Lab. Carlsberg Ser. Chim. 15: 1-30, 1924) for treatment of electrostatic interactions. On the basis of this approach, we develop an algorithm for the efficient computation of observable quantities, such as the occupancy of various ligand binding sites, and an objective statistical procedure for determining both maximum likelihood values and confidence limits of all the intrinsic thermodynamic parameters of hemoglobin. Finally, we show that the predictions of our theory are in good agreement with independent experimental observations.

The nuclear relaxation rate for the itinerant-electron antiferromagnet

1982 ◽  
Vol 60 (5) ◽  
pp. 649-653 ◽  
Author(s):  
M. Crişan ◽  
Zs. Gulácsi
Keyword(s):  
Field Theory ◽  
Relaxation Rate ◽  
Mean Field Theory ◽  
Mean Field ◽  
Band Model ◽  
Itinerant Electron ◽  
Nuclear Relaxation ◽  
The Mean ◽  
Two Band Model ◽  
Good Agreement

The relaxation rate in the nuclear magnetic resonance of the itinerant-electron antiferromagnet was calculated as a function of temperature. A good agreement with the experimental results obtained on CrB2 has been observed. The two band model for the itinerant-electron antiferromagnet for T < TN (TN is the critical temperature) and the mean field theory for the critical region have been used to calculate [Formula: see text] as a function of temperature.

Magneto—Optical Properties of Amorphous TbFe Alloys

1985 ◽  
Vol 58 ◽  
Author(s):  
M. Mansuripur ◽  
M. Ruane ◽  
P. Wolniansky ◽  
S. Chase ◽  
R. Rosenvold
Keyword(s):  
Mean Field ◽  
Hysteresis Loops ◽  
Perpendicular Magnetic Anisotropy ◽  
Field Approximation ◽  
Anisotropy Energy ◽  
Optical Methods ◽  
Mean Field Approximation ◽  
Kerr Rotation ◽  
The Mean ◽  
Good Agreement

ABSTRACTHysteresis loops and anisotropy energy constants are measured in a magneto—optical system that combines Kerr rotation and ellipticity to enhance signal strength. Temperature dependence of the polar Kerr effect is compared with the magnetization of the iron subnetwork in the mean—field approximation and good agreement is obtained. Perpendicular magnetic anisotropy is studied by magneto—optical methods, yielding the first two coefficients of the series expansion of anisotropy energy in terms of the angleof deviation from the easy axis.

Spreading of Epidemics on Scale-Free Networks with Time Delay

2012 ◽  
Vol 562-564 ◽  
pp. 1386-1389
Author(s):  
Yuan Mei Wang ◽  
Tao Li
Keyword(s):  
Field Theory ◽  
Time Delay ◽  
Mean Field Theory ◽  
Mean Field ◽  
Sir Model ◽  
Scale Free ◽  
Spreading Dynamics ◽  
Scale Free Networks ◽  
The Mean ◽  
Theoretical Results

In the SIR model once a node is cured after infection it becomes permanently immune,but we assume this immunity to be temporary. So we obtain an epidemic model with time delay on scale-free networks. Using the mean field theory the spreading threshold and the spreading dynamics is analyzed. Theoretical results indicate that the threshold is significantly dependent on the topology of scale-free networks and time delay. Numerical simulations confirmed the theoretical results.

scholarly journals Mean-field parameters of some PrxTb(1-x)Al2 compounds found via searching for the best magnetic heat capacity fitting

2021 ◽  
Vol 2090 (1) ◽  
pp. 012081
Author(s):  
J. C. G. Tedesco ◽  
V.J. Monteiro ◽  
A. M. G. Carvalho ◽  
L.P. Cardoso ◽  
A. A. Coelho
Keyword(s):  
Experimental Data ◽  
Heat Capacity ◽  
Magnetocaloric Effect ◽  
Mean Field ◽  
Heat Capacities ◽  
Field Approach ◽  
Physical Limitations ◽  
The Mean ◽  
Good Agreement

Abstract Simulations of the magnetic heat capacity of some (Pr, Tb)Al2 compounds were performed using the mean-field approach. The developed routine aims to optimize the set of mean-field parameters. The proposed algorithm calculates the sum of squared differences between the experimental points and the simulated curve and then changes the parameters in order to minimize this sum. This searching leads to consistent values that can reproduce the experimental data. The parameters found in this work reproduced the heat capacities curves of the PrxTb(1−x)Al2 compounds, x=0.25, x=0.50 and x=0.75, with good agreement. The physical limitations of the mean-field approach do not preclude analysing the results. These parameters are important because they can help to understand and calculate the magnetocaloric effect these materials can present.

scholarly journals Angular momentum and parity projected multidimensionally constrained relativistic Hartree-Bogoliubov model

2021 ◽  
Author(s):  
Kun Wang ◽  
Bingnan Lu
Keyword(s):  
Angular Momentum ◽  
Equilateral Triangle ◽  
Nuclear Physics ◽  
Mean Field ◽  
Fundamental Importance ◽  
Rigid Rotor ◽  
Angular Momentum Projection ◽  
The Mean ◽  
Moment Constraint ◽  
Good Agreement

Abstract The nuclear deformations are of fundamental importance in nuclear physics. Recently we developed a multi-dimensionally constrained relativistic Hartree-Bogoliubov (MDCRHB) model, in which all multipole deformations respecting the $V_4$ symmetry can be considered self-consistently. In this work we extend this model by incorporating the angular momentum projection (AMP) and parity projection (PP) to restore the rotational and parity symmetries broken in the mean-field level. This projected-MDCRHB (p-MDCRHB) model enables us to connect certain nuclear spectra to exotic intrinsic shapes such as triangle or tetrahedron. We present the details of the method and an exemplary calculation for $^{12}$C. We develop a triangular moment constraint to generate the triangular configurations consisting of three $\alpha$ clusters arranged as an equilateral triangle. The resulting $^{12}$C spectra are consistent with that from a triangular rigid rotor for large separations between the $\alpha$ clusters. We also calculate the $B(E2)$ and $B(E3)$ values for low-lying states and find good agreement with the experiments.

NUCLEON PROPERTIES FROM MODIFIED SIGMA MODEL

2007 ◽  
Vol 22 (14n15) ◽  
pp. 2673-2681 ◽  
Author(s):  
M. RASHDAN ◽  
M. ABU-SHADY ◽  
T. S. T. ALI
Keyword(s):  
Sigma Model ◽  
Mean Field ◽  
Field Approximation ◽  
Higher Order ◽  
Original Model ◽  
Mean Field Approximation ◽  
Field Equations ◽  
The Mean ◽  
Better Than ◽  
Good Agreement

Birse and Banerjee model is extended to include higher-order mesonic interactions. The field equations have been solved in the mean-field approximation and a good agreement with the data for the nucleon properties has been obtained. The agreement is better than that obtained by the original model of Birse and Banerjee which indicates the important of the inclusion of higher-order meson correlations.

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