Calculation of the Raman Linewidths of Lattice Modes Close to the α-β Transition in Quartz

2012 ◽  
Vol 31 (6) ◽  
pp. 741-747 ◽  
Author(s):  
Mustafa Cem Lider ◽  
Hamit Yurtseven
Keyword(s):  
Experimental Data ◽  
Critical Exponent ◽  
Power Law ◽  
Order Parameter ◽  
Quartz Crystal ◽  
Soft Mode ◽  
Energy Fluctuation ◽  
Mode Behavior ◽  
Lattice Mode ◽  
Lattice Modes

AbstractThe Raman frequencies of the lattice modes (147 cm−1 and 207 cm−1) are analyzed for the α-β transition in quartz according to a power-law formula with the critical exponent by using the experimental data. The temperature dependence of the Raman frequency is associated with the order parameter (polarization P) for this transition in the quartz crystal.The damping constant of the lattice modes studied here is calculated using the Raman frequencies at various temperatures for the α-β transition in quartz (Tc = 846 K) using the soft mode – hard mode and the energy fluctuation models. Our calculations for the damping constant (bandwidths) give an evidence that the lattice mode of the 147 cm−1 exhibits a soft mode behavior for the α-β transition in quartz.

CRITICAL BEHAVIOR OF THE SPECIFIC HEAT IN THE VICINITY OF THE TRANSITION TEMPERATURE FOR S-TRIAZINE

2009 ◽  
Vol 23 (09) ◽  
pp. 2253-2259 ◽  
Author(s):  
M. KURT ◽  
H. YURTSEVEN
Keyword(s):  
Experimental Data ◽  
Phase Transition ◽  
Transition Temperature ◽  
Critical Exponent ◽  
Specific Heat ◽  
Power Law ◽  
Order Phase Transition ◽  
Critical Behavior ◽  
First Order ◽  
Second Order Phase Transition

The critical behavior of the specific heat is studied in s-triazine ( C 3 N 3 H 3). Using the experimental data for the CP, the temperature dependence of the specific heat is analyzed according to a power-law formula and the values of the critical exponent for CP are extracted in the vicinity of the transition temperature (TC=198.07 K ). It is indicated that s-triazine undergoes a weakly first order (quasi-continuous) or second order phase transition.

scholarly journals Application of the Pippard Relations to Cyclohexane near the Melting Point

2012 ◽  
Vol 2012 ◽  
pp. 1-4 ◽  
Author(s):  
Hamit Yurtseven
Keyword(s):  
Experimental Data ◽  
Melting Point ◽  
Organic Compound ◽  
Critical Exponent ◽  
Power Law ◽  
Thermal Expansivity ◽  
Second Order ◽  
Order Transition ◽  
Thermodynamic Quantities ◽  
Second Order Transition

The Pippard relations are verified near the melting point for cyclohexane. The experimental data for the thermal expansivity is analyzed according to a power-law formula using the critical exponent and the thermodynamic quantities are calculated close to the melting point for this molecular organic compound. This applies to those compounds showing a second order transition prior to melting.

Simulation of the Eight-Dimensional Ising Model on the Creutz Cellular Automaton

1997 ◽  
Vol 08 (02) ◽  
pp. 287-292 ◽  
Author(s):  
N. Aktekin
Keyword(s):  
Magnetic Susceptibility ◽  
Renormalization Group ◽  
Critical Temperature ◽  
Ising Model ◽  
Cellular Automaton ◽  
Critical Exponent ◽  
Power Law ◽  
Order Parameter ◽  
Creutz Cellular Automaton

The eight-dimensional Ising model is simulated on the Creutz cellular automaton. By fitting the data for the order parameter to a power law with correction and by using the renormalization group prediction for its leading critical exponent as the criterion, the value of the critical temperature is found as Tc=14.898±0.010 at which the computed value of the leading critical exponent for the magnetic susceptibility is in agreement with the renormalization group prediction.

scholarly journals Low temperature Raman scattering study of barium doped lead ytterbium tantalate ceramics

2017 ◽  
Vol 07 (01) ◽  
pp. 1750003 ◽  
Author(s):  
Dibyaranjan Rout ◽  
Swetapadma Praharaj ◽  
V. Subramanian ◽  
V. Sivasubramanian
Keyword(s):  
Low Temperature ◽  
Raman Scattering ◽  
Power Law ◽  
Soft Mode ◽  
Relaxor Ferroelectric ◽  
Orthorhombic Symmetry ◽  
Complex Perovskite ◽  
Mode Behavior ◽  
Scattering Study ◽  
Cubic Structure

Raman spectra of a complex perovskite system (Pb[Formula: see text]Ba[Formula: see text](Yb[Formula: see text]Ta[Formula: see text])O3, [Formula: see text] and 0.2 have been studied at low temperature in the range of 10–250[Formula: see text]K. The fascination of the system is that it undergoes a crossover from a highly ordered antiferroelectric ([Formula: see text]) to ferroelectric ([Formula: see text]) to disordered relaxor ferroelectric ([Formula: see text]). The nature of splitting that prevails in F2g ([Formula: see text][Formula: see text]cm[Formula: see text]), F1g ([Formula: see text][Formula: see text]cm[Formula: see text]) modes and their gradual merging and disappearance with [Formula: see text] indicates an orthorhombic symmetry for [Formula: see text] and a pseudo-cubic structure for [Formula: see text]. The mode at 420[Formula: see text]cm[Formula: see text] suggests the existence of rhombohedral distortion in all the compositions. The soft mode behavior of the F2g modes has been analyzed by fitting the data with the power law [Formula: see text].

scholarly journals Polyconvex hyperelastic modeling of rubberlike materials

2021 ◽  
Vol 43 (7) ◽  
Author(s):  
Cyprian Suchocki ◽  
Stanisław Jemioło
Keyword(s):  
Experimental Data ◽  
Power Law ◽  
Curve Fitting ◽  
Constitutive Relations ◽  
Data Sets ◽  
Power Law Model ◽  
Stored Energy ◽  
Data Approximation ◽  
Exponential Power ◽  
Hyperelastic Models

AbstractIn this work a number of selected, isotropic, invariant-based hyperelastic models are analyzed. The considered constitutive relations of hyperelasticity include the model by Gent (G) and its extension, the so-called generalized Gent model (GG), the exponential-power law model (Exp-PL) and the power law model (PL). The material parameters of the models under study have been identified for eight different experimental data sets. As it has been demonstrated, the much celebrated Gent’s model does not always allow to obtain an acceptable quality of the experimental data approximation. Furthermore, it is observed that the best curve fitting quality is usually achieved when the experimentally derived conditions that were proposed by Rivlin and Saunders are fulfilled. However, it is shown that the conditions by Rivlin and Saunders are in a contradiction with the mathematical requirements of stored energy polyconvexity. A polyconvex stored energy function is assumed in order to ensure the existence of solutions to a properly defined boundary value problem and to avoid non-physical material response. It is found that in the case of the analyzed hyperelastic models the application of polyconvexity conditions leads to only a slight decrease in the curve fitting quality. When the energy polyconvexity is assumed, the best experimental data approximation is usually obtained for the PL model. Among the non-polyconvex hyperelastic models, the best curve fitting results are most frequently achieved for the GG model. However, it is shown that both the G and the GG models are problematic due to the presence of the locking effect.

The flattening phase transition in systems of trapped ions

2009 ◽  
Vol 87 (10) ◽  
pp. 1425-1435 ◽  
Author(s):  
Taunia L. L. Closson ◽  
Marc R. Roussel
Keyword(s):  
Phase Transition ◽  
Critical Exponent ◽  
Order Parameter ◽  
Ion Trap ◽  
Anisotropy Parameter ◽  
Critical Value ◽  
Trapped Ions ◽  
Dimensional Structure ◽  
Flattening Process ◽  
Second Order Phase Transition

When the anisotropy of a harmonic ion trap is increased, the ions eventually collapse into a two-dimensional structure consisting of concentric shells of ions. This collapse generally behaves like a second-order phase transition. A graph of the critical value of the anisotropy parameter vs. the number of ions displays substructure closely related to the inner-shell configurations of the clusters. The critical exponent for the order parameter of this phase transition (maximum extent in the z direction) was found computationally to have the value β = 1/2. A second critical exponent related to displacements perpendicular to the z axis was found to have the value δ = 1. Using these estimates of the critical exponents, we derive an equation that relates the amplitudes of the displacements of the ions parallel to the x–y plane to the amplitudes along the z axis during the flattening process.

scholarly journals Unbinding of Hyaluronan Accelerates the Enzymatic Activity of Bee Hyaluronidase

2011 ◽  
Vol 286 (41) ◽  
pp. 35699-35707 ◽  
Author(s):  
Attila Iliás ◽  
Károly Liliom ◽  
Brigitte Greiderer-Kleinlercher ◽  
Stephan Reitinger ◽  
Günter Lepperdinger
Keyword(s):  
Experimental Data ◽  
Quartz Crystal ◽  
Surface Loop ◽  
X Ray ◽  
Site Model ◽  
Substrate Interaction ◽  
Close Proximity ◽  
Binding Groove ◽  
The One ◽  
Best Fit

Hyaluronan (HA), a polymeric glycosaminoglycan ubiquitously present in higher animals, is hydrolyzed by hyaluronidases (HAases). Here, we used bee HAase as a model enzyme to study the HA-HAase interaction. Located in close proximity to the active center, a bulky surface loop, which appears to obstruct one end of the substrate binding groove, was found to be functionally involved in HA turnover. To better understand kinetic changes in substrate interaction, binding of high molecular weight HA to catalytically inactive HAase was monitored by means of quartz crystal microbalance technology. Replacement of the delimiting loop by a tetrapeptide interconnection increased the affinity for HA up to 100-fold, with a KD below 1 nm being the highest affinity among HA-binding proteins surveyed so far. The experimental data of HA-HAase interaction were further validated showing best fit to the theoretically proposed sequential two-site model. Besides the one, which had been shown previously in course of x-ray structure determination, a previously unrecognized binding site works in conjunction with an unbinding loop that facilitates liberation of hydrolyzed HA.

scholarly journals Speed-detachment tradeoff and its effect on track bound transport of single motor protein

2018 ◽  
Author(s):  
Mohd Suhail Rizvi
Keyword(s):  
Experimental Data ◽  
Random Walk ◽  
Power Law ◽  
Average Distance ◽  
Motor Protein ◽  
Fixed Duration ◽  
Biological Cells ◽  
Single Motor ◽  
Stochastic Nature ◽  
Time Required

AbstractThe transportation of the cargoes in biological cells is primarily driven by the motor proteins on filamentous protein tracks. The stochastic nature of the motion of motor protein often leads to its spontaneous detachment from the track. Using the available experimental data, we demonstrate a tradeoff between the speed of the motor and its rate of spontaneous detachment from the track. Further, it is also shown that this speed-detachment relation follows a power law where its exponent dictates the nature of the motor protein processivity. We utilize this information to study the motion of motor protein on track using a random-walk model. We obtain the average distance travelled in fixed duration and average time required for covering a given distance by the motor protein. These analyses reveal non-monotonic dependence of the motor protein speed on its transport and, therefore, optimal motor speeds can be identified for the time and distance controlled conditions.

Soft-Mode Behavior in the Phonon Dispersion of YS

1978 ◽  
Vol 40 (7) ◽  
pp. 465-468 ◽  
Author(s):  
P. Roedhammer ◽  
W. Reichardt ◽  
F. Holtzberg
Keyword(s):  
Soft Mode ◽  
Phonon Dispersion ◽  
Mode Behavior

TEMPERATURE DEPENDENCE OF SURFACE TENSION OF LIQUID CRYSTALS AT THE PHASE TRANSITION

1995 ◽  
Vol 09 (03n04) ◽  
pp. 237-242 ◽  
Author(s):  
R. MOLDOVAN ◽  
M. TINTARU ◽  
T. BEICA ◽  
S. FRUNZA ◽  
D. N. STOENESCU
Keyword(s):  
Experimental Data ◽  
Phase Transition ◽  
Surface Tension ◽  
Free Energy ◽  
Surface Layer ◽  
Order Parameter ◽  
Unit Area ◽  
Negative Slope ◽  
First Order ◽  
First Order Transition

The surface tension is calculated as the excess of the free energy per unit area, due to the presence of a surface layer, using Landau–de Gennes expansions, in the hypothesis of a first order transition in the bulk and taking into account the dependence of the surface free energy from the surface tilt angle. The surface order parameter is calculated and surface-ordered phase above the phase transition temperature has been found. A variety of calculated surface tension versus temperature curves with a jump at the phase transition, with positive or negative slope, well describing the experimental data from literature, have been attained.

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