RNA folding and large N matrix theory

We formulate the RNA folding problem as an N×N matrix field theory. This matrix formalism allows us to give a systematic classification of the terms in the partition function according to their topological character. The theory is set up in such a way that the limit N→∞ yields the so-called secondary structure (Hartree theory). Tertiary structure and pseudo-knots are obtained by calculating the 1/N² corrections to the partition function. We propose a generalization of the Hartree recursion relation to generate the tertiary structure.     

A random matrix approach to RNA folding with interaction

In the matrix model of RNA [G Vernizzi, H Orland and A Zee, Phys. Rev. Lett. 94, 168103 (2005)] we introduce external interactions on n bases in the action of the partition function where n ≤ L and L is the length of the polymer chain. The RNA structures found in the model can be separated into two regimes: (i) 0 ≤ α ≤ 1, n < L and 0 ≤ α < 1, n = L where unpaired and paired base structures exist and (ii) α = 1, n = L with only completely paired base structures. Figures for the genus distribution functions show differences at small lengths. We consider the situation when the strength of external perturbation is different on different bases in the polymer chain.     

Structural and thermodynamic properties of Os from first-principles calculations

We investigate the structural, thermodynamic and electronic properties of Os by plane-wave pseudopotential density functional theory method. The obtained lattice constants, bulk modulus and cell volumes per formula unit are well consistent with the available experimental data. Especially, from our calculated bulk modulus, we conclude that Os is more compressible than diamond. Moreover, the temperature induced phase transition of Os from HCP structure to FCC structure has been obtained. It is found that the transition temperature of Os at zero pressure is 2702 K. However no transition pressure is found in our calculations. The effect of bulk modulus B as well as other thermodynamic properties of Os (including the thermal expansion α and the Grüneisen constant γ) on temperatures have also been studied. Our calculated thermal expansion α=1.510×10⁻⁵ K⁻¹ and the Grüneisen constant γ=2.227 for HCP structure at room temperature agree very well with the experimental data. The density of states for HCP structure at 0 K and FCC structure at transition temperature 2702 K are also investigated in our work.     

Structure and thermodynamic properties of a polydisperse fluid in contact with a polydisperse matrix

We present expressions that allow the determination of the structural and thermodynamic properties of a polydisperse liquid mixture in contact with a polydisperse matrix; polydispersity of the fluid and of the matrix are described by distribution functions f ^f(σ) and f m (σ), where σ and σ characterize the size of the fluid and of the matrix particles. The formalism is based on the replica trick (to describe the properties of a fluid in contact with a matrix) and on the expansion of size-dependent functions in terms of orthogonal polynomials associated with the distribution functions f _f(σ) and f _m (σ). In our expressions structural and thermodynamic properties are calculated from coefficient functions (of these expansions) which are obtained from a numerical solution of the generalized replica Ornstein-Zernike equations, solved along with a suitable closure relation.     

Vibrational and thermodynamic properties of metals from a model embedded-atom potential

This work provides the first systematic test of validity of the embedded-atom potentials of Mei et al. [Phys. Rev. B 43 (1991) 4653], via a complete study of the vibrational and thermodynamic properties of isoelectronic transition (Ni, Pd, Pt) and noble (Cu, Ag, Au) metals. Phonon dispersion curves and thermal properties are studied within the quasiharmonic approximation. Results for the temperature-dependence of the lattice constants, coefficients of linear thermal expansion, isothermal and adiabatic bulk moduli, heat capacities at constant volume and constant pressure, Debye temperatures and Grüneisen parameters are presented. Electronic contribution to the specific heat is included explicitly via density-functional calculation. The calculated phonon frequencies for Ag and Cu agree well with the results from inelastic neutron scattering experiments. Despite less satisfactory agreement between calculated and measured phonon frequencies for the other four metals, isothermal and adiabatic bulk moduli and the specific heats of all metals are reproduced reasonably well by the model, while the Grüneisen parameter and Debye temperature are underestimated by about 10%. The coefficient of linear thermal expansion is underestimated with respect to measured values in most cases except for Pt and Au. The results are good for Pt up to 1000 K and for Au up to 500 K.     

Structural and thermodynamic properties of a multicomponent freely jointed hard sphere multi-Yukawa chain fluid

The product-reactant Ornstein-Zernike approach, represented by the polymer mean-spherical approximation (PMSA), is utilized to describe the structure and thermodynamic properties of the fluid of Yukawa hard sphere chain molecules. An analytical solution of the PMSA for the most general case of the multicomponent freely jointed hard sphere multi-Yukawa chain fluid is presented. As in the case of the regular MSA for the hard sphere Yukawa fluid, the problem is reduced to the solution of a set of nonlinear algebraic equations in the general case, and to a single equation in the case of the factorizable Yukawa potential coefficients. Closed form analytical expressions are presented for the contact values of the monomer-monomer radial distribution function, structure factors, internal energy, Helmholtz free energy, chemical potentials and pressure in terms of the quantities, which follows directly from the PMSA solution. By way of illustration, several different versions of the hard sphere Yukawa chain model are considered, represented by one-Yukawa chains of length m, where m = 2, 4, 8, 16. To validate the accuracy of the present theory, Monte Carlo simulations were carried out and the results are compared systematically with the theoretical results for the structure and thermodynamic properties of the system at hand. In general it is found that the theory performs very well, thus providing an analytical route to the equilibrium properties of a well defined model for chain fluids.     

Structural and thermodynamic properties of the vicinal surfaces of anharmonic crystals

Based on a correlated, or enhanced, unsymmetrized self-consistent field method, the authors study the properties of models of the vicinal surfaces of anharmonic crystals — the {, + 1} surfaces of a square lattice with nearest-neighbor interaction. Calculations are made of lattice relaxation near the surface, the effective amplitudes of atomic vibrations, and their asymmetry. The free surface energy density is obtained as a function of temperature and surface area. Its dependence on is studied. The limiting process to the {11} singular surface is examined. The possibility of generalizing the results to surfaces of three-dimensional crystals is discussed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 31–36, July, 1989.     

Structural and thermodynamic properties of wurtzite-type aluminium nitride from first-principles calculations

The lattice parameter, bulk modulus and its pressure derivative of the wurtzite-type aluminium nitride (w-AlN) are investigated by using the Cambridge Serial Total Energy Package (CASTEP) program in the framework of Density Functional Theory (DFT). The calculated results are in good agreement with the available experimental data and other theoretical results. Through the quasi-harmonic Debye model, the dependences of the normalized lattice parameters $a/a_{0}$ and $ c/c_{0}$, axial ratio $c/a$, normalized primitive-cell volume $V/V_{0}$, Debye temperature ${\it\Theta} _{\rm D} $ and heat capacity $C_{\rm V}$ on pressure $P $ and temperature $ T$ are obtained. It is found that the interlayer covalent interactions (Al-N bonds) are more (even a little) sensitive to temperature and pressure than intralayer ones (N--N bonds), which gives rise to a little lattice anisotropy in the w-AlN.     

Structural and thermodynamic properties of AlB2 compound

We employ a first-principles plane wave method with the relativistic analytic pseudopotential of Hartwigsen, Goedecker and Hutter (HGH) scheme in the frame of DFT to calculate the equilibrium lattice parameters and the thermodynamic properties of AlB₂ compound with hcp structure. The obtained lattice parameters are in good agreement with the available experimental data and those calculated by others. Through the quasi-harmonic Debye model, obtained successfully are the dependences of the normalized lattice parameters a/a₀ and c/c₀ on pressure P, the normalized primitive cell volume V/V₀ on pressure P, the variation of the thermal expansion α with pressure P and temperature T, as well as the Debye temperature \Theta_D and the heat capacity C_V on pressure P and temperature T.     

Structural and thermodynamic properties of inhomogeneous fluids in rectangular corrugated nano-pores

Based on the free-energy average method, an area-weighted effective potential is derived for rectangular corrugated nano-pore. With the obtained potential, classical density functional theory is employed to investigate the structural and thermodynamic properties of confined Lennard-Jones fluid in rectangular corrugated slit pores. Firstly, influence of pore geometry on the adsorptive potential is calculated and analyzed. Further, thermodynamic properties including excess adsorption, solvation force, surface free energy and thermodynamic response functions are systematically investigated. It is found that pore geometry can largely modulate the structure of the confined fluids, which in turn influences other thermodynamic properties. In addition, the results show that different geometric elements have different influences on the confined fluids. The work provides an effective route to investigate the effect of roughness on confined fluids. It is expected to shed light on further understanding about interfacial phenomena near rough walls, and then provide useful clues for the design and characterization of novel materials.     

Structural and thermodynamic properties of WB at high pressure and high temperature

The structure parameters and electronic structures of tungsten boride (WB) have been investigated by using the density functional theory (DFT). Our calculating results display the bulk modulus of WB are 352±2 GPa (K′₀=4.29) and 322±3 GPa (K′₀=4.21) by LDA and GGA methods, respectively. We have analyzed the probable reason of the discrepancy from the bulk modulus between theoretical and experimental results. The compression behavior of the unit cell axes is anisotropic, with the c-axis being more compressible than the a-axis. By analyzing the bond lengths information, it also demonstrated that WB has a lower compressibility at high pressure. From the partial densities of states (PDOS) of WB, we found that the Fermi lever is mostly contributed by the d states of W atom and p states of B atom and that the contributions from the s, p states of W atom and s states of B atom are small. Moreover, using the Gibbs 2 program, the thermodynamic properties of WB are obtained in a wide temperature range at high pressure for the first time in this work.     

Temperature dependence of thermodynamic properties of a polarizable potential model of water

The temperature dependence of several thermodynamic properties of water is determined at atmospheric pressure by a set of computer simulations with a polarizable potential model. It is found that the maximum of the density occurs at the correct temperature, but the decrease in density with increasing temperature is more rapid than expected for real water. Consequently, the temperature dependence of other quantities, especially that of the thermal expansion coefficient, is reproduced with some inaccuracies. The model, however, turns out to be a definitive improvement over similar non-polarizable ones, for which the density maximum is either missing or found to be shifted considerably with temperature.     

Structural, thermodynamic and electronic properties of zinc-blende AlN from first-principles calculations

Structural, thermodynamic and electronic properties of zinc-blende AlN under pressure are investigated by first-principles calculations based on the plane-wave basis set. Through the analysis of enthalpy variation of AlN in the zinc-blende (ZB) and the rock-salt (RS) structures with pressure, we find the phase transition of AlN from ZB to RS structure occurs at 6.7 GPa. By using the quasi-harmonic Debye model, we obtain the heat capacity C_V, Debye temperature Θ_D, Grüneisen parameter γ and thermal expansion coefficient α. The electronic properties including fundamental energy gaps and hydrostatic deformation potentials are investigated and the dependence of energy gaps on pressure is analysed.     

NaZn13型Fe基化合物的结构和热力学性质研究

利用Chen-Mbius晶格反演获得的原子间相互作用势,对NaZn13型Fe基金属间化合物进行原子级模拟研究.计算结果表明,Si原子和Co原子均优先占据96i晶位,Si原子和Co原子替代Fe原子后晶体平均结合能降低.随着Co含量的增加,LaFe13-x-yCoySix和NdFe13-x-yCoySix的晶格参数逐渐降低.声子态密度中,稀土原子主要激发低频模,Si原子主要激发高频模.LaFe11.5-yCoySi1.5化合物的德拜温度随Co含量的增加而增高.     

Quasi-lattice model for the thermodynamic properties and microscopic structure of molten Fe-Si alloy

The quasi-lattice model has been used to study the concentration dependant thermodynamic properties and microscopic structure of Fe-Si alloys in molten state. We have determined the free energy of mixing, excess entropy of mixing, the concentration-concentration structure factor in long wavelength limit [S_CC(0)] and the Warren-Cowley short range order parameter (α₁) of Fe-Si liquid alloy at 1873 K. The observed asymmetry in the properties of mixing of Fe-Si alloy in molten state is successfully explained on the basis of the quasi-lattice model. The analysis suggests that the Fe₂Si complexes are most likely to exist in the liquid state and are strongly interacting in nature. The theoretical analysis suggests that the pairwise interaction energies between the species depend considerably on temperature and the alloy is more ordered towards Fe rich region.     

一类海-气振子模型的微扰解

文章创建一个求解关于海-气振子模型非线性方程的渐近方法,并且基于一类海-气振子模型,借助于改进的微扰方法,首先按时滞参数进行展开,然后对两小参数的相对值分为三种情形进行讨论,最后利用微分不等式理论得到了问题解的一致有效的渐近展开式.