scholarly journals Harmonic Maps in Connection of Phase Transitions with Higher Dimensional Potential Wells

2019 ◽  
Vol 40 (5) ◽  
pp. 781-810
Author(s):  
Fanghua Lin ◽  
Changyou Wang
Keyword(s):  
Phase Transitions ◽  
Harmonic Maps ◽  
Potential Wells ◽  
Higher Dimensional

NMR · NQR and DTA · DSC Studies of Phase Transitions in Pyridinium Tetrachloropalladate(II) and Pyridinium Tetrachloroplatinate(II)

1998 ◽  
Vol 53 (6-7) ◽  
pp. 419-426 ◽  
Author(s):  
Tetsuo Asaji ◽  
Keizo Horiuchi ◽  
Takehiko Chiba ◽  
Takashige Shimizu ◽  
Ryuichi Ikeda
Keyword(s):  
Phase Transitions ◽  
Low Temperatures ◽  
Structural Phase ◽  
Orientational Order ◽  
Second Order ◽  
Order Transition ◽  
Spin Lattice Relaxation ◽  
Potential Wells ◽  
H Nmr ◽  
Second Order Transition

Abstract From the measurements of DTA • DSC and the temperature dependences of 35Cl NQR frequencies, phase transitions were detected at 150 K, 168 K, and 172 K for (pyH)2 [PtCl4], and at 241 K for (PyH)2 [PdCl4]. In order to elucidate the motional state of the constituent ions in the crystals in connection with the structural phase transitions, the 35Cl NQR and 1H NMR spin-lattice relaxation times and the second moment of the 1H NMR line were measured as functions of temperature. For both compounds, the potential wells for the cationic reorientation are suggested to be highly nonequivalent at low temperatures. Above 168 K, the pyridinium ions in (pyH)2[PtCl4] are expected to reorient between almost equivalent potential wells. As for (pyH)2[PdCl4], it is expected that the orientational order of the cation still remains even above the second order transition at 241 K. A change of the potential curve from two-unequal to three-unequal wells is proposed as a possible mechanism of the second order transition. The activation energies for the cationic motion in the respective model potential are derived for both compounds at high and low temperatures.

PHASE TRANSITIONS IN HIGHER DIMENSIONAL COSMOLOGY

2010 ◽  
Vol 25 (01) ◽  
pp. 113-122
Author(s):  
RIZWAN UL HAQ ANSARI ◽  
P. K. SURESH
Keyword(s):  
Phase Transitions ◽  
Early Universe ◽  
Higher Dimensions ◽  
Temperature Dependent ◽  
Loop Correction ◽  
Massive Scalar Field ◽  
Five Dimensions ◽  
Higher Dimensional Cosmology ◽  
Higher Dimensional ◽  
The One

We have considered five-dimensional massive scalar field coupled to gravity and evaluated the one-loop effective potential in higher dimensions. It is demonstrated that nonminimally coupled φ4 theory can be regularized in five dimensions. Temperature dependent one-loop correction and critical temperature βc are computed. The phase transitions in the early universe depend on the space–time curvature R and scalar gravitational coupling ξ. A brief discussion of symmetry restoration is also presented and the nature of phase transitions in the early universe is found to be of second order.

scholarly journals QUASI-ONE DIMENSIONAL FLUIDS THAT EXHIBIT HIGHER DIMENSIONAL BEHAVIOR

2010 ◽  
Vol 24 (25n26) ◽  
pp. 5051-5059 ◽  
Author(s):  
SILVINA M. GATICA ◽  
M. MERCEDES CALBI ◽  
GEORGE STAN ◽  
R. ANDREEA TRASCA ◽  
MILTON W. COLE
Keyword(s):  
Carbon Nanotubes ◽  
Phase Transitions ◽  
Finite Temperature ◽  
Review Paper ◽  
Two Dimensional ◽  
Reduced Dimensionality ◽  
Narrow Channels ◽  
One Dimensional ◽  
Higher Dimensional ◽  
Effective Dimensionality

Fluids confined within narrow channels exhibit a variety of phases and phase transitions associated with their reduced dimensionality. In this review paper, we illustrate the crossover from quasi-one dimensional to higher effective dimensionality behavior of fluids adsorbed within different carbon nanotubes geometries. In the single nanotube geometry, no phase transitions can occur at finite temperature. Instead, we identify a crossover from a quasi-one dimensional to a two dimensional behavior of the adsorbate. In bundles of nanotubes, phase transitions at finite temperature arise from the transverse coupling of interactions between channels.

2H NMR Study on Phase Transitions and Crystal Dynamics of p-Chloro- and p-Bromobenzyl Alcohols

2002 ◽  
Vol 57 (6-7) ◽  
pp. 388-394 ◽  
Author(s):  
Motohiro Mizuno ◽  
Masanori Hamada ◽  
Tomonori Ida ◽  
Masahiko Suhara ◽  
Masao Hashimoto
Keyword(s):  
Relaxation Time ◽  
Phase Transitions ◽  
Nmr Spectra ◽  
Spin Lattice Relaxation ◽  
Temperature Phase ◽  
Hydrogen Atoms ◽  
Potential Wells ◽  
H Nmr ◽  
Nmr Study ◽  
Crystal Dynamics

Two phase transitions of 4-chlorobenzyl alcohol (pCBA) and 4-bromobenzyl alcohol (pBBA), from the low-temperature phase (LTP) to the intermediate-temperature phase (ITP) and from ITP to the room-temperature phase (RTP), were investigated by 2H NMR and differential scanning calorimetry (DSC). The crystal dynamics in each phase were studied using the 2H NMR spectra, the spin-lattice relaxation time (T1) and the relaxation time of quadrupole order (T1Q) for the samples, where the hydrogen of the -OH group was selectively deutrated. The 2H NMR 1 of both crystals in the RTP were dominated by the fluctuation of the electric field gradient at 2H nucleus caused by vibrational motions of the -CH2OH group. In the LTP of both crystals, the fast jump of hydrogen atoms between the two sites corresponding approximately to the positions of the hydroxyl hydrogen atoms in the RTP and LTP were found from 2H NMR spectra. The results of T1 and T1Q in the LTP revealed that the jump of hydrogen atoms occurs in asymmetric potential wells and that these potential wells gradually approach symmetric ones with increasing temperature on the high-temperature side in the LTP

A short proof of the McCoy conjecture in higher-dimensional classical continuous models of Kac types

2017 ◽  
Vol 31 (10) ◽  
pp. 1750111 ◽  
Author(s):  
Assane Lo
Keyword(s):  
Phase Transitions ◽  
Correlation Functions ◽  
Short Proof ◽  
Higher Dimensional ◽  
Continuous Models ◽  
Higher Derivatives ◽  
Derivatives Of

We consider the pressure and correlation functions of d-dimensional classical continuous models of Kac type. We prove that if the kth moments of the potential exist, then the system cannot have phase transitions of order lower than k. We also obtain a better formula for the higher derivatives of the pressure that leads to more precise estimates of the truncated correlations.

The gradient theory of phase transitions for systems with two potential wells

1989 ◽  
Vol 111 (1-2) ◽  
pp. 89-102 ◽  
Author(s):  
Irene Fonseca ◽  
Luc Tartar
Keyword(s):  
Phase Transitions ◽  
Interfacial Area ◽  
Gradient Theory ◽  
Compactness Result ◽  
Potential Wells ◽  
The Family ◽  
Two Phases ◽  
Image Position ◽  
Nonconvex Functional ◽  
Vector Valued

SynopsisIn this paper we generalise the gradient theory of phase transitions to the vector valued case. We consider the family of perturbationsof the nonconvex functionalwhere W:RN→R supports two phases and N ≧1. We obtain the Γ(L1(Ω))-limit of the sequenceMoreover, we improve a compactness result ensuring the existence of a subsequence of minimisers of Eε(·) converging in L1(Ω) to a minimiser of E0(·) with minimal interfacial area.

Polytopes of Higher Dimension in the Nature

2018 ◽  
pp. 1-45
Keyword(s):  
Experimental Data ◽  
Phase Transitions ◽  
Chemical Compounds ◽  
Higher Dimension ◽  
Higher Dimensional ◽  
The Creation ◽  
Structure Of Matter

Areas of research into the phenomena of nature in which the influence of polytopes of higher dimension is described in this chapter. These include studies of the structures of many chemical compounds whose molecules exhibit the properties of polytopes of higher dimension. This leads to the creation of higher-dimensional stereochemistry. Phase transitions of the second kind are accompanied by a change in the symmetry of the structure of matter, the description of which, in agreement with the experimental data, requires the attraction of spaces of higher dimension. Elementary cells of quasicrystals, having the form of polytopic prismahedrons, are given (polytopes of higher dimension). The structure of DNA as sequence of the higher dimensional polytopes are given.

Electron Microscopy of Graphite Intercalation Compounds

1982 ◽  
Vol 40 ◽  
pp. 544-545
Author(s):  
G. Timp ◽  
L. Salamanca-Riba ◽  
L.W. Hobbs ◽  
G. Dresselhaus ◽  
M.S. Dresselhaus
Keyword(s):  
Electron Microscopy ◽  
Phase Transitions ◽  
Domain Wall ◽  
Intercalation Compounds ◽  
Lattice Plane ◽  
Wall Model ◽  
Graphite Intercalation Compounds ◽  
Fundamental Symmetry ◽  
Graphite Intercalation

Electron microscopy can be used to study structures and phase transitions occurring in graphite intercalations compounds. The fundamental symmetry in graphite intercalation compounds is the staging periodicity whereby each intercalate layer is separated by n graphite layers, n denoting the stage index. The currently accepted model for intercalation proposed by Herold and Daumas assumes that the sample contains equal amounts of intercalant between any two graphite layers and staged regions are confined to domains. Specifically, in a stage 2 compound, the Herold-Daumas domain wall model predicts a pleated lattice plane structure.

Multiple phase transitions investigated by high-speed TEM

1990 ◽  
Vol 48 (4) ◽  
pp. 550-551
Author(s):  
Oleg Bostanjoglo ◽  
Peter Thomsen-Schmidt
Keyword(s):  
Phase Transitions ◽  
High Speed ◽  
Short Exposure ◽  
Semiconductor Film ◽  
Time Resolved ◽  
Short Exposure Time ◽  
Multiple Phase ◽  
Model Substance ◽  
History Of ◽  
Electron Image

Thin GexTe1-x (x = 0.15-0.8) were studied as a model substance of a composite semiconductor film, in addition being of interest for optical storage material. Two complementary modes of time-resolved TEM were used to trace the phase transitions, induced by an attached Q-switched (50 ns FWHM) and frequency doubled (532 nm) Nd:YAG laser. The laser radiation was focused onto the specimen within the TEM to a 20 μm spot (FWHM). Discrete intermediate states were visualized by short-exposure time doubleframe imaging /1,2/. The full history of a transformation was gained by tracking the electron image intensity with photomultiplier and storage oscilloscopes (space/time resolution 100 nm/3 ns) /3/. In order to avoid radiation damage by the probing electron beam to detector and specimen, the beam is pulsed in this continuous mode of time-resolved TEM,too.Short events ( <2 μs) are followed by illuminating with an extended single electron pulse (fig. 1c)

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