scholarly journals Analysis of the integrated intensity of the central peaks calculated as a function of temperature in the ferroelectric phase of lithium tantalate

2018 ◽  
Vol 22 (Suppl. 1) ◽  
pp. 221-227
Author(s):  
Ali Kiracı ◽  
Hamit Yurtseven
Keyword(s):  
Order Parameter ◽  
Ferroelectric Phase ◽  
Brillouin Scattering ◽  
Dynamic Properties ◽  
Mean Field Theory ◽  
Mean Field ◽  
Central Peak ◽  
Academic Disciplines ◽  
Inverse Relaxation Time ◽  
Integrated Intensity

The integrated intensity of the central peak is calculated as a function of temperature in the ferroelectric phase (T < TC) of nearly stoichiometric LiTaO3. This calculation is performed using the temperature dependence of the order parameter obtained from the mean field theory at temperatures lower than the transition temperature TC (TC = 963 K) of this crystal. The calculated values of the order parameter (squared) are fitted to the integrated intensity of the central peaks as observed from the Raman and Brillouin scattering experiments as reported in the literature in the ferroelectric phase of nearly stoichiometric LiTaO3. Our results are in good agreement with the observed behavior of LiTaO3 crystal. Because of the applications of LiTaO3 in several academic disciplines including the material science and thermal science, it is beneficial to investigate dynamic properties of this crystal such as the damping constant, inverse relaxation time and the activation energy as also we studied here.

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.

Radiative transfer in layered media and its connection to the O'Doherty-Anstey formula

Geophysics ◽  
2005 ◽  
Vol 70 (1) ◽  
pp. T1-T11 ◽  
Author(s):  
Matthew M. Haney ◽  
Kasper van Wijk ◽  
Roel Snieder
Keyword(s):  
Radiative Transfer ◽  
Layered Medium ◽  
Dynamic Properties ◽  
Mean Field Theory ◽  
Mean Field ◽  
Mean Free Path ◽  
Scalar Wave ◽  
Coherent Wave ◽  
Diffusive Flow ◽  
Basic Level

We examine radiative transfer theory, which accounts for the multiple scattering of waves in a layered medium composed of randomly placed thin beds excited by a 1D source. At its most basic level, radiative transfer predicts that the wavefield separates into a coherent, or wavelike, part and an incoherent, or diffusive, flow after a length scale known as a mean free path. The dynamic properties of the coherent and incoherent wavefield are linked. For 1D Rayleigh scatterers, or thin beds, we show that the exponential decay of the coherent wave predicted by radiative transfer corresponds to the decay predicted by the O'Doherty–Anstey formula. This equivalence reveals an underlying relationship between radiative transfer and mean field theory. Finite-difference simulations of the scalar wave equation with randomly placed thin beds demonstrate the diffusive behavior of the incoherent energy at late times.

Order Parameter, Mean-Field Theory, and the Ideal Bose Gas

1969 ◽  
Vol 188 (1) ◽  
pp. 522-525 ◽  
Author(s):  
M. Schick ◽  
P. R. Zilsel
Keyword(s):  
Field Theory ◽  
Order Parameter ◽  
Mean Field Theory ◽  
Mean Field ◽  
Bose Gas ◽  
Ideal Bose Gas ◽  
The Ideal

A FIRST ORDER PHASE TRANSITION IN ISING FERRIMAGNETS

1995 ◽  
Vol 09 (21) ◽  
pp. 1347-1351 ◽  
Author(s):  
HASAN M. AL MUKADAM ◽  
DIMO I. UZUNOV
Keyword(s):  
Phase Transition ◽  
Order Parameter ◽  
Mean Field Theory ◽  
Mean Field ◽  
First Order ◽  
First Order Phase Transition ◽  
Exchange Constants ◽  
The Mean ◽  
First Order Phase ◽  
Ising Spins

The mean field theory is used for the analysis of a two-sublattice system of Ising spins, which describes ferro-, antiferro-, and ferrimagnetic orderings. It is proven that the phase transition in these systems is of a first order when the exchange constants of the sublattices are different. The free energy, the order parameter profiles and the latent heat of the phase transition are calculated for almost equivalent sublattices.

SURFACE ROTATIONAL DISORDERING IN CRYSTALLINE C60

1997 ◽  
Vol 04 (05) ◽  
pp. 859-861 ◽  
Author(s):  
D. PASSERONE ◽  
E. TOSATTI
Keyword(s):  
Order Parameter ◽  
Mean Field Theory ◽  
Mean Field ◽  
Rotational Transition ◽  
Layer By Layer ◽  
Energy Term ◽  
First Order ◽  
Potential Energy Term ◽  
Body Potential ◽  
Order Surface

We present a theory of surface rotational disordering of crystalline fullerene. Realistic intermolecular interactions are implemented, in a layer-by-layer mean field theory. The crucial new ingredient turns out to be a one-body potential energy term, or "crystal field," is totally different at the surface, therefore locally frustrating bulk order. This frustration causes a severe surface order parameter reduction, and a first order surface rotational disordering transition, well below the corresponding bulk one. Preliminary results are in agreement with recent experiments, confirming a first order surface rotational transition of C 60(111) at a transition temperature lower than the bulk one.

Novel Epitaxial Growth and Surface Order-Disorder Transitions of CU3AU(110) and CU3AU(111)

1991 ◽  
Vol 237 ◽  
Author(s):  
J.C.A. Huang ◽  
J. A. Dura ◽  
C. P. Flynn
Keyword(s):  
Mean Field Theory ◽  
Mean Field ◽  
High Energy ◽  
Buffer Layers ◽  
Surface Layers ◽  
Sapphire Substrates ◽  
Integrated Intensity ◽  
Initial Deposition ◽  
Atomically Flat ◽  
Kinetics Of

AbstractWe report the results of a reflection high energy electron diffraction (RHEED) study on the order-disorder transitions at the (111) and (110) surface of Cu3Au. Our Cu3Au films were epitaxially grown on sapphire substrates with bcc (Nb or Mo-Cr) buffer layers. The (111) and (110) surfaces of Cu3Au are atomically flat as indicated by the RHEED patterns. We use the normalized integrated intensity of the superstructure streaks to measure the long range order parameter. We observed that the surface layers of both (110) and (111) Cu3Au exhibit an apparently continuous order-disorder transition, close to that predicted by mean field theory [5]. The kinetics of surface ordering also were monitored by RHEED after initial deposition of disordered layers, 2 MLs thick, on the ordered Cu3Au templates. In studies of the surface reordering process we find that the RHEED pattern is almost entirely sensitive to the surface layer alone.

scholarly journals The constructive role of diversity in the global response of coupled neuron systems

2010 ◽  
Vol 368 (1933) ◽  
pp. 5619-5632 ◽  
Author(s):  
Toni Pérez ◽  
Claudio R. Mirasso ◽  
Raúl Toral ◽  
James D. Gunton
Keyword(s):  
Field Theory ◽  
Order Parameter ◽  
Mean Field Theory ◽  
Mean Field ◽  
External Signal ◽  
Global Response ◽  
Diffusive Coupling ◽  
External Modulation ◽  
Collective Response

We study the effect that the heterogeneity present among the elements of an ensemble of coupled excitable neurons has on the collective response of the system to an external signal. We consider two different interaction scenarios, one in which the neurons are diffusively coupled and another in which the neurons interact via pulse-like signals. We find that the type of interaction between the neurons has a crucial role in determining the response of the system to the external modulation. We develop a mean-field theory based on an order parameter expansion that quantitatively reproduces the numerical results in the case of diffusive coupling.

Detailed study of the phase transition in [Ni(H2O)6](NO3)2·(15-crown-5)·H2O and analysis in terms of mean-field theory

2011 ◽  
Vol 67 (2) ◽  
pp. 130-143 ◽  
Author(s):  
Maxime A. Siegler ◽  
Sean Parkin ◽  
Ross J. Angel ◽  
Carolyn Pratt Brock
Keyword(s):  
High Temperature ◽  
Order Parameter ◽  
Energy Surface ◽  
Lattice Water Molecule ◽  
Mean Field Theory ◽  
Mean Field ◽  
Structural Evolution ◽  
High Temperature Phase ◽  
Group Symmetry ◽  
Temperature Phase

The transition between 190 and 200 K in [Ni(H2O)6](NO3)2·(15-crown-5)·H2O has been followed by determining the structure at 22 temperatures in the range 90–273 K. The structural change is a zone-boundary transition with a critical point at (½, 0, ½) in the Brillouin zone of the high-temperature phase; both phases have space-group symmetry P21 but the volume of the unit cell is halved when a crystal is heated through the transition. The only obvious disorder in the high-temperature phase is of the lattice water molecule, which occupies two sites; some disorder persists below the transition. The greatest changes in the structure below the transition are the rotations of one of the two 15-crown-5 molecules and of one of the two nitrate ions; above the transition the two molecules are related by symmetry as are the two ions. Below the transition these two rotation angles evolve linearly with one another, and can thus be associated with a single order parameter that describes the structural evolution. The evolution of the spontaneous strain arising from the transition does not, however, follow the same evolution as the structural order parameter. This observation indicates that the transition cannot be described in terms of a Landau-type expansion that is characterized by a single order parameter, perhaps because the potential-energy surface for this essentially molecular crystal is more complicated than for the inorganic and framework structures in which such simple behaviour is observed.

scholarly journals STATISTICS OF STATISTICIANS: CRITICAL MASS OF STATISTICS AND OPERATIONAL RESEARCH GROUPS

2012 ◽  
Vol 16 ◽  
pp. 29-40
Author(s):  
RALPH KENNA ◽  
BERTRAND BERCHE
Keyword(s):  
Operational Research ◽  
Statistical Physics ◽  
Critical Mass ◽  
Mean Field Theory ◽  
Mean Field ◽  
Academic Disciplines ◽  
Research Quality ◽  
Research Assessment ◽  
Research Groups ◽  
Average Maximum

Using a recently developed model, inspired by mean field theory in statistical physics, and data from the UK's Research Assessment Exercise, we analyse the relationship between the qualities of statistics and operational research groups and the quantities of researchers in them. Similar to other academic disciplines, we provide evidence for a linear dependency of quality on quantity up to an upper critical mass, which is interpreted as the average maximum number of colleagues with whom a researcher can communicate meaningfully within a research group. The model also predicts a lower critical mass, which research groups should strive to achieve to avoid extinction. For statistics and operational research, the lower critical mass is estimated to be 9 ± 3. The upper critical mass, beyond which research quality does not significantly depend on group size, is 17 ± 6.

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