On the local structure of the phase separation line in the two-dimensional Ising system

We investigate the structure of the phase separation line between the pure phases in the two-dimensional Ising model, the liquid and vapor phase in lattice gas language, at low temperatures. The fluctuations in the location of this line are known to diverge in the thermodynamic limit, something which is also believed to happen to the continuum liquid-vapor interface in three dimensions (in the absence of the gravitational field). We show that despite this global divergence it is possible to define precisely the local structure of the phase separation line. This has a finite, exponentially small, width at low temperatures which is related by a central limit theorem⁽¹⁾ to the width of the global fluctuations on the appropriate (divergent) length scale. The latter has been computed explicitly⁽²⁾ for all temperatures below the critical temperatureT _c, where it diverges as (T _c –T)^–1/2. We also prove a Gibbs formula for the surface tension at low temperature, which relates it to the local structure of the phase separation line.Supported in part by NSF grant No. M^rPHY 78-15920 and MCS78-01885.On leave from: Departement de Physique Théorique, Université de Louvain, Belgium.     

Dynamics of fluctuations for quantum lattice systems

For short range interactions and forL ¹-space clustering states it is proved that there exists a bonafide time evolution on the set of normal fluctuations. This dynamics is applied to derive the notion of equilibrium state of the algebra of fluctuations.     

Row transfer matrix spectra of cyclic solid-on-solid lattice models

The eigenvalue spectra of cyclic solid-on-solid (CSOS) row transfer matrices are studied. An equivalence is established between the inversion identity and the Bethe ansatz functional equations and these equations are solved in the thermodynamic limit by a Wiener-Hopf perturbation technique for the bands of leading excitations. TheL-state CSOS model, with crossing parameter=s/L, possesses a 2(L – s)-fold degenerate largest eigenvalue corresponding to the 2(L – s) coexisting phases. The expressions for the largest eigenvalue and free energy coincide with those of the eight-vertex model. The string excitations for 2s < L and 2s > L admit different classifications and are treated separately. The correlation length is calculated in both regimes, yielding the critical exponentv=L/2s, in agreement with the scaling relations.     

Roughness and dynamics of a contact line of a viscous fluid on a disordered substrate

We have studied the roughness and the dynamics of the contact line of a viscous liquid on a disordered substrate. We have used photolithographic techniques to obtain a controlled disorder with a correlation length ξ = 10μm. Liquids with different viscosity were used: water and aqueous glycerol solution. We have found that the roughness W of the contact line depends neither on the viscosity nor on the velocity v of the contact line for v in the range 0.2-20μm/s. W is found to scale with the length L of the line as L ^ζ with a roughness exponent ζ = 0.51±0.03. This value is similar to the one obtained with superfluid helium. In the present experiment, we have checked that the motion of the contact line is actually overdamped, so that the phenomenological equation first proposed by Ertas and Kardar should be relevant. However, our measurement of ζ is in disagreement with the predicted value ζ = 0.39. We have also analyzed the avalanche-like motion of the contact line. We find that the size distribution does not follow a power law dependence. Received 18 April 2002     

The analytical potential energy function of flue gas SO2（X1A1）

The equilibrium structure of flue gas SO2 is optimized using the density functional theory （DFT）/B3P86 method and CC-PV5Z basis. The result shows that it has a bent （C2v, X1A1） ground state structure with an angle of 119.1184°. The vibronic frequencies and the force constants are also calculated. Based on the principles of atomic and molecular reaction statics （AMIIS）, the possible electronic states and reasonable dissociation limits for the ground state of SO2 molecule are determined. The potential functions of SO and 02 are fitted by the modified Murrell-Sorbie＋c6 （M-S＋c6） potential function and the fitted parameters, the force constants and the spectroscopic constants are obtained, which are all close to the experimental values. The analytic potential energy function of the SO2 （X1A1） molecule is derived using the many-body expansion theory. The contour liues are constructed, which show the static properties of SO2 （XIA1）, such as the equilibrium structure, the lowest energies, the most possible reaction channel, etc.     

Ab initio calculations of the deformation potentials for intervalley phonon-assisted transitions in АIIIВV crystals with sphalerite structure

Completely self-consistent ab initio calculations of scattering of electrons between the lowest minima of the conduction band by short-wavelength phonons are performed for the first time for a group of А ^III В ^V semiconductor crystals. The structure constants, electron and vibrational spectra, and probabilities of scattering are calculated for the crystals from unified positions within the electronic density functional method. The theory does not involve any phenomenological assumptions on positions of minima in the conduction band, effective carrier masses, interatomic forces, or scattering probabilities. The electron-phonon coupling constants (the deformation potentials) for actual Γ−X, Γ−L, and X−L transitions for scattering between the nonequivalent X−X and L−L valleys in the conduction bands of AlP, AlAs, AlSb, GaP, GaAs, GaSb, InP, InAs, and InSb crystals with sphalerite structure are calculated. Results obtained are compared with theoretical calculations within the phenomenological rigid ion model and with those performed by the selfconsistent frozen phonon method.     

The vicinity of an equilibrium three-phase contact line using density-functional theory: density profiles normal to the fluid interface

The paper by Nold et al. [Phys. Fluids 26 (7), 072001 (2014)] examined density profiles and the micro-scale structure of an equilibrium three-phase (liquid–vapour–solid) contact line in the immediate vicinity of the wall using elements from the statistical mechanics of classical fluids, namely density-functional theory. The present research note, building on the above work, further contributes to our understanding of the nanoscale structure of a contact line by quantifying the strong dependence of the liquid–vapour density profile on the normal distance to the interface, when compared to the dependence on the vertical distance to the substrate. A recent study by Benet et al. [J. Phys. Chem. C 118 (38), 22079 (2014)] has shown that this could explain the emergence of a film-height-dependent surface tension close to the wall, with implications for the Frumkin–Derjaguin theory.     

微观相场法模拟Ni75Al5.3V19.7 中L12和D022结构反位缺陷的演化

运用微观相场法研究Ni₇₅Al_5.3V_19.7合金沉淀过程中L1₂结构和D0₂₂结构反位缺陷发现：在沉淀初期,L1₂结构反位缺陷Al_Ni,V_Ni,Ni_Al,D0₂₂结构反位缺陷V_Ni,Al_Ni关键词： 微观相场 反位缺陷 L1₂结构')" href="#">L1₂结构 D0₂₂结构')" href="#">D0₂₂结构     

On the Spectral Dynamics of the Deformation Tensor and New A Priori Estimates for the 3D Euler Equations

In this paper we study the dynamics of eigenvalues of the deformation tensor for solutions of the 3D incompressible Euler equations. Using the evolution equation of the L² norm of spectra, we deduce new a priori estimates of the L² norm of vorticity. As an immediate corollary of the estimate we obtain a new sufficient condition of L² norm control of vorticity. We also obtain decay in time estimates of the ratios of the eigenvalues. In the remarks we discuss what these estimates suggest in the study of searching initial data leading to possible finite time singularities. We find that the dynamical behaviors of L² norm of vorticity are controlled completely by the second largest eigenvalue of the deformation tensor. Part of this work was done while the author was visiting CSCAMM, University of Maryland, USA. The author would like to thank to Professor E. Tadmor for his hospitality     

Random matrix structure of nuclear shell model Hamiltonian matrices and comparison with an atomic example

We present a comprehensive analysis of the structure of Hamiltonian matrices based on visualization of the matrices in three dimensions as well as in terms of measures for GOE, banded and two-body random matrix ensembles (TBRE). We have considered two nuclear shell model examples, ²²Na with J^p T = 2⁺0\ensuremath J^{\pi} T = 2^+0 and ²⁴Mg with J^p T = 0⁺0\ensuremath J^{\pi} T = 0^+0 and, for comparison we have also considered the SmI atomic example. It is clearly established that the matrices are neither GOE nor banded. For the TBRE structure we have examined the correlations between diagonal elements and eigenvalues, fluctuations in the basis states variances and structure of the two-body part of the Hamiltonian in the eigenvalue basis. Unlike the atomic example, nuclear examples show that the nuclear shell model Hamiltonians can be well represented by TBRE.     

Momentum transport and torque scaling in Taylor-Couette flow from an analogy with turbulent convection

We generalize an analogy between rotating and stratified shear flows. This analogy is summarized in Table 1. We use this analogy in the unstable case (centrifugally unstable flow vs. convection) to compute the torque in Taylor-Couette configuration, as a function of the Reynolds number. At low Reynolds numbers, when most of the dissipation comes from the mean flow, we predict that the non-dimensional torque G = T/ν² L, where L is the cylinder length, scales with Reynolds number R and gap width η, G = 1.46η^3/2(1 - η)^-7/4 R ^3/2. At larger Reynolds number, velocity fluctuations become non-negligible in the dissipation. In these regimes, there is no exact power law dependence the torque versus Reynolds. Instead, we obtain logarithmic corrections to the classical ultra-hard (exponent 2) regimes: G = 0.50 . These predictions are found to be in excellent agreement with avail-able experimental data. Predictions for scaling of velocity fluctuations are also provided. Received 7 June 2001 and Received in final form 7 December 2001     

Fluctuations and lack of self-averaging in the kinetics of domain growth

The fluctuations occurring when an initially disordered system is quenched at timet=0 to a state, where in equilibrium it is ordered, are studied with a scaling theory. Both the mean-sizel(t) ^d of thed-dimensional ordered domains and their fluctuations in size are found to increase with the same power of the time; their relative size fluctuations are independent of the total volumeL ^d of the system. This lack of self-averaging is tested for both the Ising model and the ⁴ model on the square lattice. Both models exhibit the same lawl(t)=(Rt) ^x withx=1/2, although the ⁴ model has soft walls. However, spurious results withx1/2 are obtained if bad pseudorandom numbers are used, and if the numbern of independent runs is too small (n itself should be of the order of 10³). We also predict a critical singularity of the rateR(1–T/T _c) ^v(z–1/x),v being the correlation length exponent,z the dynamic exponent.Also quenches to the critical temperatureT _c itself are considered, and a related lack of self-averaging in equilibrium computer simulations is pointed out for quantities sampled from thermodynamic fluctuation relations.     

K α L 1 satellite multiplet structure of photon-excited chlorine atoms

Summary An attempt is made to study theK _α L ¹ satellite multiplet structure of chlorine atoms in different compounds by photon excitation. A comparison of the averageK _α L ¹ group energy shift from the diagram line with those based on Dirac-Fock evaluations with different number ofM-shell electrons shows a reasonable agreement. The intensity ratios are found to be higher than those studied in Mg compounds in general.     

Electron paramagnetic resonance of spin-variable metallomesogens [Fe<Emphasis Type="Italic">L</Emphasis><Subscript>2</Subscript>]<Emphasis Type="Italic">X</Emphasis> (<Emphasis Type="Italic">X</Emphasis> = PF<Subscript>6</Subscript>, SCN)

Significant differences in the manifestation of spin-crossover properties of the mesogen compounds [FeL ₂]X with oxysalicylidene-N′-ethyl-N-ethylenediamine ligands L and anions X = PF₆⁻ and SCH⁻ have been found by means of electron paramagnetic resonance. The electron paramagnetic resonance data and the quantum-chemical calculation within the density functional theory enables us to establish that the observed specific features are associated with the incorporation of the SCH⁻ ion into the first coordination sphere of the Fe(III) ion. The role of the transition of the material to the liquid-state phase in the formation of a low-dimensional (two-dimensional) structure with stronger intermolecular interactions has been revealed.     

Modeling and computation of two phase geometric biomembranes using surface finite elements

Biomembranes consisting of multiple lipids may involve phase separation phenomena leading to coexisting domains of different lipid compositions. The modeling of such biomembranes involves an elastic or bending energy together with a line energy associated with the phase interfaces. This leads to a free boundary problem for the phase interface on the unknown equilibrium surface which minimizes an energy functional subject to volume and area constraints. In this paper we propose a new computational tool for computing equilibria based on an L² relaxation flow for the total energy in which the line energy is approximated by a surface Ginzburg–Landau phase field functional. The relaxation dynamics couple a nonlinear fourth order geometric evolution equation of Willmore flow type for the membrane with a surface Allen–Cahn equation describing the lateral decomposition. A novel system is derived involving second order elliptic operators where the field variables are the positions of material points of the surface, the mean curvature vector and the surface phase field function. The resulting variational formulation uses H¹ spaces, and we employ triangulated surfaces and H¹ conforming quadratic surface finite elements for approximating solutions. Together with a semi-implicit time discretization of the evolution equations an iterative scheme is obtained essentially requiring linear solvers only. Numerical experiments are presented which exhibit convergence and the power of this new method for two component geometric biomembranes by computing equilibria such as dumbbells, discocytes and starfishes with lateral phase separation.     

On the spectra of Schrödinger operators

We give two formulas for the lowest point in the spectrum of the Schrödinger operatorL=–(d/dt)p(d/dt)+q, where the coefficientsp andq are real-valued, bounded, uniformly continuous functions on the real line. We determine whether or not is an eigenvalue forL in terms of a set of probability measures on the maximal ideal space of theC ^*-algebra generated by the translations ofp andq.Research supported in part by the National Science Foundation under Grant DMS-910496     

The values of <L 2> in diatomic molecules: implications for adiabatic and molecular fine structure calculations

The possibility of using calculated ab initio values of <L ²> to assess convergence of second order sums in molecular fine structure parameters is investigated for several diatomic molecules with ³Σ^- ground states. Values of <L ²> for a number of molecules in ¹Σ⁺ states have also been obtained. The calculated values of <L ²> are in general very large, especially for non-hydride molecules, and they show a marked dependence on the internuclear separation R. The implications of these large values of <L ²> are discussed both for the calculation of molecular fine structure parameters (where the convergence criterion is seen to be of little use) and for the adiabatic corrections often needed in discussing isotopic effects. In this latter context, ab initio values of have also been calculated and found to be an important term in adiabatic corrections, contrary to some assertions in the literature. The implications of the strong dependence of <L ²> on the internuclear separation are also discussed.     

Solutions of the Fokker-Planck equation for a double-well potential in terms of matrix continued fractions

Solutions of the Fokker-Planck (Kramers) equation in position-velocity space for the double-well potentiald ₂x²/2+d₄x⁴/4 in terms of matrix continued fractions are derived. It is shown that the method is also applicable to a Boltzmann equation with a BGK collision operator. Results of eigenvalues and of the Fourier transform of correlation functions are presented explicitly. The lowest nonzero eigenvalue is compared with the escape rate in the weak noise limit for various damping constants and the susceptibility is compared with the zero-friction-limit result.