scholarly journals UNIFIED TREATMENT OF A+B→0 AND A+A→0 CHEMICAL REACTIONS THROUGH THOMPSON'S APPROACH

1999 ◽  
Vol 13 (22n23) ◽  
pp. 829-836 ◽  
Author(s):  
CLÁUDIO NASSIF ◽  
P. R. SILVA
Keyword(s):  
Chemical Reactions ◽  
Mean Field ◽  
Reaction Rates ◽  
Rigorous Results ◽  
Critical Dimensions ◽  
Long Wavelength ◽  
Diffusion Limited ◽  
First Case ◽  
Long Time ◽  
The Mean

In this work we propose an action to describe diffusion limited chemical reactions belonging to various classes of universality. This action is treated through Thompson's approach and can encompass both cases where we have segregation as in the A + B →0 reaction, as well as the simplest one, namely the A + A →0 reaction. Our results for long-time and long-wavelength behaviors of the species concentrations and reaction rates agree with exact results of Peliti for A + A →0 reaction and rigorous results of Bramson and Lebowitz for A + B →0 reaction, with equal initial concentrations. The different classes of universality are reflected by the obtained upper critical dimensions varying continuously from d c =2 in the first case to d c =4 in the last one. Just as at the upper critical dimensions, we find universal logarithmic corrections to the mean field behavior.

Long Time Estimates in the Mean Field Limit

2008 ◽  
Vol 190 (3) ◽  
pp. 517-547 ◽  
Author(s):  
E. Caglioti ◽  
F. Rousset
Keyword(s):  
Mean Field ◽  
Field Limit ◽  
Mean Field Limit ◽  
Time Estimates ◽  
Long Time ◽  
The Mean

CRITICAL DIMENSIONS OF SYSTEMS WITH JOINT MULTICRITICAL AND LIFSHITZ-POINT-LIKE BEHAVIOR

2011 ◽  
Vol 25 (22) ◽  
pp. 1839-1845 ◽  
Author(s):  
ARTEM V. BABICH ◽  
LESYA N. KITCENKO ◽  
VYACHESLAV F. KLEPIKOV
Keyword(s):  
Field Theory ◽  
Critical Phenomena ◽  
Critical Points ◽  
Order Parameter ◽  
Mean Field Theory ◽  
Mean Field ◽  
Critical Dimensions ◽  
Lifshitz Point ◽  
The Mean ◽  
Derivatives Of

In this article, we consider a model that allows one to describe critical phenomena in systems with higher powers and derivatives of order parameter. The systems considered have critical points with joint multicritical and Lifshitz-point-like properties. We assess the lower and upper critical dimensions of these systems. These calculation enable us to find the fluctuation region where the mean field theory description does not work.

ON PHASE TRANSITIONS ON BETHE LATTICES

1994 ◽  
Vol 08 (25) ◽  
pp. 1587-1590 ◽  
Author(s):  
RAFFAELLA BURIONI ◽  
DAVIDE CASSI
Keyword(s):  
Phase Transitions ◽  
Critical Temperature ◽  
Simple Formula ◽  
Mean Field ◽  
Scaling Relations ◽  
Long Range Order ◽  
Rigorous Results ◽  
Tree Structures ◽  
Bethe Lattices ◽  
The Mean

Starting from some recent rigorous results about correlation functions of statistical model on tree structures, we analyze the nature of phase transitions occurring on Bethe lattices, showing the lack of long range order and the purely geometrical origin of the thermodynamic singularities. This approach gives a very simple formula for the critical temperature for any model with compact symmetry group and immediately leads to the value 1 for the critical exponent γ. The “geometrical” critical behavior only partially coincides with the mean field solution and violates the usual scaling relations.

scholarly journals Simultaneous Chemical Reactions Effect on Dispersion of a Solute in Peristaltic Propulsion of a Newtonian Fluid in an Inclined Channel with Wall Properties

2019 ◽  
Vol 24 (3) ◽  
pp. 527-538
Author(s):  
M.Y. Dhange ◽  
G.C. Sankad
Keyword(s):  
Viscous Fluid ◽  
Chemical Reactions ◽  
Effective Coefficient ◽  
Long Wavelength ◽  
Inclined Channel ◽  
Heterogeneous Chemical ◽  
Wall Properties ◽  
Uniform Channel ◽  
The Mean ◽  
Heterogeneous Chemical Reactions

Abstract In this paper, the dispersion of a solute in the peristaltic propulsion of an incompressible and viscous fluid through a permeable medium under the influence of wall properties with simultaneous homogeneous, heterogeneous chemical reactions in an inclined uniform channel has been studied. The issue is studied through conditions of Taylor’s limit and long wavelength hypothesis. The mean effective coefficient of scattering expression is computed and outcomes are interpreted physically through graphs.

scholarly journals Continuum dynamics of the intention field under weakly cohesive social interaction

2017 ◽  
Vol 27 (01) ◽  
pp. 159-182 ◽  
Author(s):  
Pierre Degond ◽  
Jian-Guo Liu ◽  
Sara Merino-Aceituno ◽  
Thomas Tardiveau
Keyword(s):  
Planck Equation ◽  
Type Equation ◽  
Opinion Formation ◽  
Time Dynamics ◽  
First Case ◽  
Long Time ◽  
The Mean ◽  
Continuum Dynamics ◽  
Long Time Dynamics ◽  
Fokker Planck

We investigate the long-time dynamics of an opinion formation model inspired by a work by Borghesi, Bouchaud and Jensen. First, we derive a Fokker–Planck-type equation under the assumption that interactions between individuals produce little consensus of opinion (grazing collision approximation). Second, we study conditions under which the Fokker–Planck equation has non-trivial equilibria and derive the macroscopic limit (corresponding to the long-time dynamics and spatially localized interactions) for the evolution of the mean opinion. Finally, we compare two different types of interaction rates: the original one given in the work of Borghesi, Bouchaud and Jensen (symmetric binary interactions) and one inspired from works by Motsch and Tadmor (non-symmetric binary interactions). We show that the first case leads to a conservative model for the density of the mean opinion whereas the second case leads to a non-conservative equation. We also show that the speed at which consensus is reached asymptotically for these two rates has fairly different density dependence.

Well-posedness and asymptotic behavior of an aggregation model with intrinsic interactions on sphere and other manifolds

2021 ◽  
pp. 1-53
Author(s):  
Razvan C. Fetecau ◽  
Hansol Park ◽  
Francesco S. Patacchini
Keyword(s):  
Riemannian Manifolds ◽  
Collective Behavior ◽  
Mean Field ◽  
Sufficient Conditions ◽  
Well Posedness ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Long Time ◽  
The Mean ◽  
Particle Approximation

We investigate a model for collective behavior with intrinsic interactions on Riemannian manifolds. We establish the well-posedness of measure-valued solutions (defined via mass transport) on sphere, as well as investigate the mean-field particle approximation. We study the long-time behavior of solutions to the model on sphere, where the primary goal is to establish sufficient conditions for a consensus state to form asymptotically. Well-posedness of solutions and the formation of consensus are also investigated for other manifolds (e.g., a hypercylinder).

scholarly journals WRITING ELECTRONIC FERROMAGNETIC STATES IN A HIGH-TEMPERATURE PARAMAGNETIC NUCLEAR SPIN SYSTEM

2011 ◽  
Vol 09 (04) ◽  
pp. 1047-1056 ◽  
Author(s):  
D. O. SOARES-PINTO ◽  
J. TELES ◽  
A. M. SOUZA ◽  
E. R. DEAZEVEDO ◽  
R. S. SARTHOUR ◽  
...  
Keyword(s):  
Magnetic Field ◽  
High Temperature ◽  
Mean Field ◽  
Field Approximation ◽  
Order Transition ◽  
Mean Field Approximation ◽  
Temperature Hysteresis ◽  
First Case ◽  
The Matrix ◽  
The Mean

In this paper, we use Nuclear Magnetic Resonance (NMR) to write electronic states of a ferromagnetic system into high-temperature paramagnetic nuclear spins. Through the control of phase and duration of radio frequency pulses, we set the NMR density matrix populations, and apply the technique of quantum state tomography to experimentally obtain the matrix elements of the system, from which we calculate the temperature dependence of magnetization for different magnetic fields. The effects of the variation of temperature and magnetic field over the populations can be mapped in the angles of spin rotations, carried out by the RF pulses. The experimental results are compared to the Brillouin functions of ferromagnetic ordered systems in the mean field approximation for two cases: the mean field is given by (i) B = B0 + λM and (ii) B = B0 + λM + λ′M3, where B0 is the external magnetic field, and λ, λ′ are mean field parameters. The first case exhibits second order transition, whereas the second case has first order transition with temperature hysteresis. The NMR simulations are in good agreement with the magnetic predictions.

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