On a specific heat-phonon spectrum inversion problem. Exact solution, unique existence theorem and Riemann hypothesis

1990 ◽  
Vol 147 (8-9) ◽  
pp. 445-449 ◽  
Author(s):  
Xianxi Dai ◽  
Xinwen Xu ◽  
Jiqiong Dai
Keyword(s):  
Exact Solution ◽  
Specific Heat ◽  
Existence Theorem ◽  
Phonon Spectrum ◽  
Riemann Hypothesis ◽  
Inversion Problem ◽  
Unique Existence ◽  
Spectrum Inversion

A unified solution of the specific-heat–phonon spectrum inversion problem

2003 ◽  
Vol 61 (6) ◽  
pp. 723-728 ◽  
Author(s):  
DengMing Ming ◽  
Tao Wen ◽  
JiXin Dai ◽  
W. E Evenson ◽  
XianXi Dai
Keyword(s):  
Specific Heat ◽  
Phonon Spectrum ◽  
Inversion Problem ◽  
Spectrum Inversion

New exact solution formula for specific heat-phonon spectrum inversion and its application in studies of superconductivity

2000 ◽  
Vol 341-348 ◽  
pp. 1919-1920
Author(s):  
Tao Wen ◽  
JiXin Dai ◽  
Dengming Ming ◽  
William E. Evenson ◽  
Dai Xianxi
Keyword(s):  
Exact Solution ◽  
Specific Heat ◽  
Phonon Spectrum ◽  
Spectrum Inversion

Exact solution of the specific-heat–phonon spectrum inversion from the Möbius inverse formula

2000 ◽  
Vol 62 (3) ◽  
pp. R3019-R3022 ◽  
Author(s):  
DengMing Ming ◽  
Tao Wen ◽  
JiXin Dai ◽  
Xianxi Dai ◽  
William E. Evenson
Keyword(s):  
Exact Solution ◽  
Specific Heat ◽  
Phonon Spectrum ◽  
Möbius Inverse ◽  
Spectrum Inversion

Some Inverse Problems in the Studies of High Tc Superconductivity

1999 ◽  
Vol 13 (29n31) ◽  
pp. 3431-3433
Author(s):  
Dai XianXi ◽  
Wen Tao ◽  
Ma GuiCun ◽  
JiXin Dai
Keyword(s):  
Specific Heat ◽  
Current Density ◽  
Inversion Problem ◽  
High Tc Superconductors ◽  
High Tc ◽  
Maximum Current Density ◽  
Relaxation Problem ◽  
Maximum Current ◽  
Density Problem ◽  
Spectrum Inversion

Two topics are reviewed or studied in this paper: 1. The specific heat-photon spectrum inversion problem; 2. The inverse relaxation problem in high Tc superconductors and finding its maximum current density problem.

A concrete realization of specific heat-phonon spectrum inversion for YBCO

1999 ◽  
Vol 264 (1) ◽  
pp. 68-73 ◽  
Author(s):  
Dai XianXi ◽  
Tao Wen ◽  
GuiCun Ma ◽  
JiXin Dai
Keyword(s):  
Specific Heat ◽  
Phonon Spectrum ◽  
Concrete Realization ◽  
Spectrum Inversion

Phonon spectrum and specific heat of silicon nanowires

2007 ◽  
Vol 102 (10) ◽  
pp. 104303 ◽  
Author(s):  
Y. Zhang ◽  
J. X. Cao ◽  
Y. Xiao ◽  
X. H. Yan
Keyword(s):  
Specific Heat ◽  
Silicon Nanowires ◽  
Phonon Spectrum

scholarly journals THE PHONON SPECTRUM OF THE OCTAGONAL TILING

1993 ◽  
Vol 07 (06n07) ◽  
pp. 1505-1525 ◽  
Author(s):  
J. LOS ◽  
T. JANSSEN ◽  
F. GÄHLER
Keyword(s):  
Specific Heat ◽  
Density Of States ◽  
Phonon Spectrum ◽  
Low Frequency ◽  
Debye Model ◽  
Square Lattice ◽  
Total Density ◽  
Unit Cells ◽  
Linear Behaviour ◽  
Total Density Of States

A study of the phonon spectrum of the octagonal tiling is presented, by calculating and analysing the properties of the spectrum of perfect and randomized commensurate approximants with unit cells containing up to 8119 vertices. The total density of states, obtained by numerical integration over the Brillouin zone, exhibits much structure, and in the low frequency range of the spectrum there is deviation from the normal linear behaviour in the form of pseudogaps. For randomized approximants these pseudogaps disappear and the density of states is globally smoothened. It turns out that the widths of the gaps in the dispersion vanish in the low frequency limit. Therefore the scaling behaviour of the lowest branches tends to the behaviour of an absolutely continuous spectrum, which is not the case at higher frequencies. As an application, the vibrational specific heat of the different tiling models is calculated and compared to the specific heat of a square lattice and of a Debye model.

scholarly journals Exact Solution to the Extended Zwanzig Model for Quasi-Sigmoidal Chemically Induced Denaturation Profiles: Specific Heat and Configurational Entropy

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
G. E. Aguilar-Pineda ◽  
L. Olivares-Quiroz
Keyword(s):  
Exact Solution ◽  
Analytical Solution ◽  
Specific Heat ◽  
Configurational Entropy ◽  
Naturally Occurring ◽  
Thermodynamic Potentials ◽  
Chemically Induced ◽  
Denaturation Profile ◽  
Average Internal Energy ◽  
Proteins And Peptides

Temperature and chemically induced denaturation comprise two of the most characteristic mechanisms to achieve the passage from the native state N to any of the unstructured states Dj in the denatured ensemble in proteins and peptides. In this work we present a full analytical solution for the configurational partition function 𝒵qs of a homopolymer chain poly-X in the extended Zwanzig model (EZM) for a quasisigmoidal denaturation profile. This solution is built up from an EZM exact solution in the case where the fraction α of native contacts follows exact linear dependence on denaturant’s concentration ζ; thus an analytical solution for 𝒵L in the case of an exact linear denaturation profile is also provided. A recently established connection between the number ν of potential nonnative conformations per residue and temperature-independent helical propensity ω complements the model in order to identify specific proteinogenic poly-X chains, where X represents any of the twenty naturally occurring aminoacid residues. From 𝒵qs, equilibrium thermodynamic potentials like entropy 𝒮 and average internal energy 〈E〉 and thermodynamic susceptibilities like specific heat C𝓋 are calculated for poly-valine (poly-V) and poly-alanine (poly-A) chains. The influence of the rate at which native contacts denature as function of ζ on thermodynamic stability is also discussed.

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