scholarly journals DEFORMED QUANTUM STATISTICS IN TWO DIMENSIONS

2009 ◽  
Vol 23 (02) ◽  
pp. 235-250 ◽  
Author(s):  
A. LAVAGNO ◽  
P. NARAYANA SWAMY
Keyword(s):  
Specific Heat ◽  
Thermodynamic Functions ◽  
Occupation Number ◽  
Ideal Gas ◽  
Two Dimensions ◽  
Fixed Temperature ◽  
Standard Case ◽  
Deformed Oscillator ◽  
Spatial Dimensions ◽  
Deformed Oscillator Algebra

It is known from the early work of May in 1964 that ideal Bose gas do not exhibit condensation phenomenon in two dimensions. On the other hand, it is also known that the thermostatistics arising from q-deformed oscillator algebra has no connection with the spatial dimensions of the system. Our recent work concerns the study of important thermodynamic functions such as the entropy, occupation number, internal energy and specific heat in ordinary three spatial dimensions, where we established that such thermostatistics is developed by consistently replacing the ordinary thermodynamic derivatives by the Jackson derivatives. The thermostatistics of q-deformed bosons and fermions in two spatial dimensions is an unresolved question that is the subject of this investigation. We study the principal thermodynamic functions of both bosons and fermions in the two-dimensional q-deformed formalism and we find that, different from the standard case, the specific heat of q-boson and q-fermion ideal gas, at fixed temperature and number of particles, are no longer identical.

INTERPOLATING STATISTICS AND q-DEFORMED OSCILLATOR ALGEBRAS

2006 ◽  
Vol 20 (06) ◽  
pp. 697-713 ◽  
Author(s):  
P. NARAYANA SWAMY
Keyword(s):  
Quantum Groups ◽  
Thermodynamic Functions ◽  
Oscillator Algebra ◽  
Fermi Statistics ◽  
Deformed Oscillator ◽  
Deformed Oscillator Algebra ◽  
Continuous Interpolation ◽  
Outstanding Issue ◽  
Derivatives Of ◽  
Oscillator Algebras

The idea that a system obeying interpolating statistics can be described by a deformed oscillator algebra, or quantum groups, has been an outstanding issue. We are able to demonstrate that a q-deformed oscillator algebra can be used to describe the statistics of particles which provide a continuous interpolation between Bose and Fermi statistics. We show that the generalized intermediate statistics splits into Boson-like and Fermion-like regimes, each described by a unique oscillator algebra. The thermostatistics of Boson-like particles is described by employing q-calculus based on the Jackson derivative while the Fermion-like particles are described by ordinary derivatives of thermodynamics. Thermodynamic functions for systems of both types are determined and examined.

scholarly journals Temperature dependence of the specific heat and thermodynamic functions AК1М2 alloy, doped strontium

2019 ◽  
Vol 21 (1) ◽  
pp. 35-42 ◽  
Author(s):  
I. N. Ganiev ◽  
S. E. Otajonov ◽  
N. F. Ibrohimov ◽  
M. Mahmudov
Keyword(s):  
Heat Capacity ◽  
Gibbs Energy ◽  
Specific Heat ◽  
Temperature Dependence ◽  
Specific Heat Capacity ◽  
Thermodynamic Functions ◽  
Inverse Relationship ◽  
Alloying Element ◽  
Enthalpy And Entropy ◽  
Increasing Temperature

In the heat «cooling» investigated the temperature dependence of the specific heat capacity and thermodynamic functions doped strontium alloy AK1М2 in the range 298,15—900 K. Mathematical models are obtained that describe the change in these properties of alloys in the temperature range 298.15—900 K, as well as on the concentration of the doping component. It was found that with increasing temperature, specific heat capacity, enthalpy and entropy alloys increase, and the concentration up to 0.5 wt.% of the alloying element decreases. Gibbs energy values have an inverse relationship, i.e., temperature — decreases the content of alloying component — is up to 0.5 wt.% growing.

scholarly journals Exact solution and the multidimensional Godunov scheme for the acoustic equations

2022 ◽  
Author(s):  
Wasilij Barsukow ◽  
Christian Klingenberg
Keyword(s):  
Exact Solution ◽  
Mach Number ◽  
Euler Equations ◽  
Two Dimensions ◽  
Finite Volume Scheme ◽  
Godunov Scheme ◽  
Low Mach Number ◽  
Low Mach Number Limit ◽  
Acoustic Equations ◽  
Spatial Dimensions

The acoustic equations derived as a linearization of the Euler equations are a valuable system for studies of multi-dimensional solutions. Additionally they possess a low Mach number limit analogous to that of the Euler equations. Aiming at understanding the behaviour of the multi-dimensional Godunov scheme in this limit, first the exact solution of the corresponding Cauchy problem in three spatial dimensions is derived. The appearance of logarithmic singularities in the exact solution of the 4-quadrant Riemann Problem in two dimensions is discussed. The solution formulae are then used to obtain the multidimensional Godunov finite volume scheme in two dimensions. It is shown to be superior to the dimensionally split upwind/Roe scheme concerning its domain of stability and ability to resolve multi-dimensional Riemann problems. It is shown experimentally and theoretically that despite taking into account multi-dimensional information it is, however, not able to resolve the low Mach number limit.

Influence of Lithium on Specific Heat and Changes in the Thermodynamic Functions of Aluminum Alloy AB1

2020 ◽  
Vol 58 (1) ◽  
pp. 58-63 ◽  
Author(s):  
I. N. Ganiev ◽  
M. T. Nazarova ◽  
U. Sh. Yakubov ◽  
A. G. Safarov ◽  
M. Z. Kurbonova
Keyword(s):  
Aluminum Alloy ◽  
Specific Heat ◽  
Thermodynamic Functions

Temperature Dependence of the Specific Heat and the Changes in the Thermodynamic Functions of a Bismuth-Bearing AZh4.5 Alloy

2020 ◽  
Vol 2020 (1) ◽  
pp. 17-24 ◽  
Author(s):  
I. N. Ganiev ◽  
A. G. Safarov ◽  
F. R. Odinaev ◽  
U. Sh. Yakubov ◽  
K. Kabutov
Keyword(s):  
Specific Heat ◽  
Temperature Dependence ◽  
Thermodynamic Functions

Specific heat and related thermodynamic functions of undercooled Cu-Ni and Au melts

1996 ◽  
Vol 205-207 ◽  
pp. 425-429 ◽  
Author(s):  
G. Wilde ◽  
C. Mitsch ◽  
G.P. Görler ◽  
R. Willnecker
Keyword(s):  
Specific Heat ◽  
Thermodynamic Functions

Kraftkonstanten, mittlere Schwingungsamplituden, Coriolis-Kopplungskonstanten und thermodynamische Funktionen der Moleküle WOCl4 und WOBr4 / Force Constants, Mean Amplitudes, Coriolis Coupling Constants, Thermodynamic Functions, WOCl4 , WOBr4

1974 ◽  
Vol 29 (4) ◽  
pp. 620-623 ◽  
Author(s):  
W. Brockner ◽  
H. Hovdan ◽  
S. J. Cyvin
Keyword(s):  
Thermodynamic Functions ◽  
Ideal Gas ◽  
Force Constants ◽  
Coupling Constants ◽  
Coriolis Coupling ◽  
Mean Amplitudes Of Vibration ◽  
Amplitude Correction ◽  
Different Temperatures ◽  
Harmonic Oscillator Approximation ◽  
The Mean

A normal co-ordinate analysis of the molecules W 0Cl4 and WOBr4 has been carried out following W ilson’s FG matrix method. Valence force constants based on known (WOCl4) and estimated (WOBr4) molecular parameters have been evaluated. The results support the assignment of the known Raman spectra of W0Cl4 . Also the mean amplitudes of vibration and the perpendicular amplitude correction coefficients K have been computed for the temperatures T = 0 and T = 298 °K. Furthermore the Coriolis coupling constants of the ζz(EaxEb)- type have been determined. Some thermodynamic functions have also been calculated for an ideal gas state at one atmosphere pressure and different temperatures using the rigid rotor harmonic oscillator approximation.

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