Experimental free energy surface reconstruction from single-molecule force spectroscopy using Jarzynski's equality

We used the atomic force microscope to manipulate and unfold individual molecules of the titin I27 domain and reconstructed its free energy surface using Jarzynski's equality. The free energy surface for both stretching and unfolding was reconstructed using an exact formula that relates the nonequilibrium work fluctuations to the molecular free energy. In addition, the unfolding free energy barrier, i.e., the activation energy, was directly obtained from experimental data for the first time. This Letter demonstrates that Jarzynski's equality can be used to analyze nonequilibrium single-molecule experiments, and to obtain the free energy surfaces for molecular systems, including interactions for which only nonequilibrium work can be measured.     

Photo- and electroluminescence of nitrogen isoelectronic traps in GaAs1–xPx

The variation with temperature of the charge on the surface of NaCl single crystals has been measured directly by means of vibrating capacitor probe. The charge is negative at room temperature, in agreement with theory based on values of the free energy of vacancy formation, decreases with increase of temperature in two stages to a zero value at the isoelectric temperature, and then becomes positive. Values of isoelectric temperature obtained on surfaces are consistent with those obtained by experiments on charged dislocations, which suggests that surfaces could be used to obtain accurate values of the free energy of formation of cation and anion vacancies.     

Crystalline structure of the Au(1 1 1) surface revealed by stereographic intensity DEPES maps

The intensity of elastically backscattered electrons at the primary electron beam energy 1.9 keV was used to obtain a stereographic map of Au(1 1 1) by means of the directional elastic peak electron spectroscopy (DEPES). An experimental result is compared with the theoretical data obtained by using multiple scattering calculations (MS) performed for both not-reconstructed and model-reconstructed clusters. The lateral lattice misfit of the first layer leads to quantitative changes of theoretical intensities showing a sensitivity of DEPES to the short atomic chain axial order. This comparison proves that a main contribution of the experimental contrast originates from a higher background level. Moreover an anisotropy of the inelastic mean free path is discussed in the paper.     

An extension of the small-slope approximation for rough surface scattering

Solutions are derived for scattering from a rough one-dimensional pressure-release surface in the form of a functional series in the surface slope. These solutions are obtained by solving an integral equation of the first kind for the surface potential to obtain a representation for the scattering amplitude. It is shown that the subsequent expansion of terms occurring in the scattering amplitude to obtain a functional series in the slope does not yield a unique result. The result obtained contains a free parameter that may be arbitrarily selected. Thus, this result is an extension or generalization of the small-slope approximation of Voronovich (1985 Sov. Phys.-JETP 62 65-70) that differs at second order in the slope from his result. It is also shown that the free parameter can be selected such that each term of the functional series is reciprocal and exhibits a limiting grazing angle dependence consistent with the requirements of flux conservation and the absence of boundary waves. A new formulation of the leading terms of the small-slope expansions is derived and is used to explore the conditions under which the two expansions reduce to the Kirchhoff approximation. Finally, a numerical example is presented to demonstrate that the extended approximation provides corrections that are important for near grazing scatter.     

A comprehensive approach to the free vibration analysis of rectangular plates by use of the method of superposition

The authors have found the above techniques to constitute a powerful means for solving rectangular plate problems. At the time of writing, solutions for plates with two adjacent simply supported edges and two adjacent free edges have been obtained. The first 20 eigen-values for plates with all edges clamped have also been determined for a full range of aspect ratio and they are shown to be accurate to within less than one half of one percent. It will be appreciated that solutions for any combination of clamped-simply supported edge conditions can easily be obtained from the all-clamped solution by simply deleting appropriate solutions from the all-clamped combination. In Figure 2 contour lines for first mode vibration of a plate with two adjacent clamped and two adjacent simply supported edges is presented. The higher density of the contour lines along the simply supported edges will be noted.The method of superposition is currently being used by the authors to good advantage to obtain solutions of any desired degree of accuracy to all of the problems discussed. It is found to be easily utilized and unlike more complicated methods is readily comprehensible to the practicing engineer. Eigenvalues for all modes, aspect ratios, and boundary conditions are readily obtained. Modal shapes are expressed in terms of familiar analytic functions. Results of these studies will be made available in future publications.     

Condensate fraction of asymmetric three-component Fermi gas

In this paper, we investigate the condensate fraction （CF） of fermionic pairs in the BCS-BEC crossover for three- component Fermi gas with both asymmetric interactions and unequal chemical potentials in two-dimensional free space. By using the functional-path-integral method, we have analytically derived the number densities and bound-state energy, from which the off-diagonal long-range order is analyzed in terms of the asymptotic behavior of the two-body density matrix. The explicit formula of CF is obtained as a function of the bound-state energy and population imbalance. It is demonstrated that the CF spectrum with respect to the bound-state energy can be used to characterize the quantum phase transition between the two kinds of Sarma phases as well as the transition from three-component to two-component superfluid. Moreover we obtain the same analytic formula of CF in the BCS superfluid phase as that of homogeneous Fermi gas with equal chemical potentials.     

On the validity of the capillarity approximation in the rate theory of homogeneous nucleation

An Einstein model is used to calculate the internal vibrational free energy of approximately spherical fcc crystallites as a function of crystallite size at T/θ = 1. It is found that the free energy per surface atom does not become convergent until a size of about 3 × 10⁷ atoms is reached. The excess free energy at convergence is used to define the macroscopic surface tension for use in the capillarity approximation. The internal free energy of microcrystallites containing of the order of 100 atoms is fortuitously well described by the capillarity approximation. A good estimate of the total free energy of the microcrystallite (nucleus) is obtained from the capillarity approximation only by adding the contributions from free translation and rotation and the replacement partition function.     

Changes in wetting and energetic properties of glass caused by deposition of different lipid layers

An investigation of wetting and energetic properties of different lipid layers deposited on the glass surface was carried out by contact angles measurements and determination of the apparent surface free energy. The topography of the lipid layers was also determined with the help of atomic force microscopy (AFM). Two synthetic phospholipids were chosen for these studies, having the same phosphatidylcholine headgroup bound to the apolar part composed either by two saturated chains (1,2-dipalmitoyl-sn-glycero-3-phospshocholine - DPPC) or two unsaturated chains (1,2-dioleoyl-sn-glycero-3-phosphocholine - DOPC) and one lipid (1,2,3-trihexadecanoyl-sn-glycerol - tripalmitoylglycerol - TPG). The lipid layers, from the 1st to the 5th statistical monolayer, were deposited on the glass surface from chloroform solutions by spreading.The apparent surface free energy of the deposited layers was determined by contact angles measurements (advancing and receding) for three probe liquids (diiodomethane, water, and formamide), and then two concepts of interfacial interactions were applied. In the contact angle hysteresis approach (CAH) the apparent total surface free energy was calculated from the advancing and receding contact angles and surface tension of probe liquids. In the Lifshitz-van der Waals/acid-base approach (LWAB) the total surface free energy was calculated from the determined components of the energy, which were obtained from the advancing contact angles of the probe liquids only. Comparison of the results obtained by two approaches provided more information about the changes in the hydrophobicity/hydrophilicity of the layers depending on the number of monolayers and kind of the lipid deposited on the glass surface.It was found that the most visible changes in the surface free energy took place for the first two statistical monolayers irrespectively of the kind of the lipid used. Additionally, in all cases periodic oscillations from layer-to-layer in the lipid surface free energy were observed. The changes in the surface free energy correlated with those in the topography and roughness of lipid layers.     

基于格林函数法的奇型Mathieu-Gaussian光束

根据光束传播的独立性和叠加性原理,引入了一组能够产生第一类(2n+2阶)奇型Mathieu-Gaussian光束的虚光源点.利用虚源点技术和格林函数法,计算得到第一类奇型Mathieu-Gaussian光束的严格解析积分表达式.利用该表达式得到了轴上光场分布的积分解析解.以三阶非旁轴修正为例,得到了第一类奇型Mathieu-Gaussian光束保留到三阶非旁轴修正项的轴上光场分布精确解.     

Self-consistent theory of the surface thermodynamic properties of strongly anharmonic crystals

The nonlinear integral equations of the asymmetric self-consistent field method are applied to a semiinfinite, strongly anharmonic crystal bounded by a gaseous phase. These equations are used to obtain the self-consistent potential for crystal atoms close to the surface, and through this potential, the surface free energy is obtained. The nonlinear integral equation is reduced to a set of transcendental equations and a method is given for the solving the latter.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 80–84, March, 1984.     

The gauged O(3) sigma model: Schrödinger representation and Hamilton-Jacobi formulation

We first study a free particle on an (n−1)-sphere in an extended phase space, where the originally second-class Hamiltonian and constraints are now in strong involution. This allows for a Schrödinger representation and a Hamilton-Jacobi formulation of the model. We thereby obtain the free particle energy spectrum corresponding to that of a rigid rotator. We extend these considerations to a modified version of the field theoretical O(3) nonlinear sigma model, and obtain the corresponding energy spectrum as well as BRST Lagrangian.     

Irreducible finite-size effects in the surface free energy of NaCl crystals from crystal-nucleation data

In this Letter we report a simulation study in which we compare the solid-liquid interfacial free energy of NaCl at coexistence, gamma_{LS}, with the value that follows from the height of the homogeneous nucleation barrier. The two estimates differ by more than 100%. Smaller discrepancies are found for gamma_{LS} of hard-sphere and of Lennard-Jones particles. We consider a variety of possible causes for this discrepancy and conclude that it is due to a finite-size effect that cannot be corrected for by any simple thermodynamic procedure. By taking into account the finite-size effects of gamma_{LS} obtained in real nucleation experiments, we obtain quantitative agreement between gamma_{LS} estimated in the simulations and derived from the experiments. Our finding suggests that most published solid-liquid surface free energies derived from nucleation experiments will have to be revised.     

采用球面波叠加法还原自由声场的方法

为解决非自由声场中近场声全息重建时,干扰声在目标声源表面产生的散射影响,提出一种基于球面波叠加法的自由场还原技术。该技术首先采用基于球面波叠加法的声场分离技术获得向内和向外传播的声场,然后以目标声源的表面导纳作为边界条件,实现目标声源辐射声和散射声的分离,从而获得等效于自由声场的测量条件。该技术为准确实现非自由声场中的噪声源识别创造了条件。文中首先详细描述了该技术的基本原理,并提出一种最优球面波展开项数选取方法,最后通过数值仿真说明了该技术的有效性。结果表明:在频率较低时,散射声影响较小,采用声场分离技术和自由场还原技术效果相当;但随着频率升高,散射声影响逐步增强,必须采用自由场还原技术才能准确获得目标声源辐射声。     

Compressible Ising double chains

We obtain exact expressions for the free energy and the magnetic susceptibility in zero field of a compressible double Ising chain with first and second neighbour interactions. The chain is supposed to be made of rigid rods which move like dumbbells in an elastic harmonic potential. The exchange interactions along the direction of the chain are linear functions of the spacing between rods. The effective spin hamiltonian of the double chain involves short-range two and four-spin interactions. Due to the existence of compensation points, we obtain regions of peculiar thermodynamic properties in the pressure-temperature phase diagram.     

Phase diagram of the infinite range Ashkin-Teller model

The free energy functional of the infinite range ferromagnetic Ashkin-Teller model is examined in detail. The analytical study of the stability conditions is used to obtain the phase diagram.     

Thermodynamic States of the Mixed Spin 1/2 and Spin 1 Hexagonal Nanowire System Obtained from a Seven-Site Cluster Within an Improved Mean Field Approximation

The mean field approximation results in the mixedspin 1/2 Ising model and spin 1 Blume-Capel model, in the hexagonal nanowire system, are obtained from the Bogoliubov inequality. The Gibbs free energy, magnetization, and critical frontiers are obtained. Besides the stable branches of the order parameters, we obtain the metastable and unstable parts of these curves and also find phase transitions of the metastable branches of the order parameters. The classification of the stable, metastable, and unstable states is made by comparing the free energy values of these states.     

The string of variable density: Further results

We analyze the problem of calculating the solutions and the spectrum of a string with arbitrary density and fixed ends. We build a perturbative scheme which uses a basis of WKB-type functions and obtain explicit expressions for the eigenvalues and eigenfunctions of the string. Using this approach we show that it is possible to derive the asymptotic (high energy) behavior of the string, obtaining explicit expressions for the first three coefficients (the first two can also be obtained with the WKB method). Finally, using an iterative approach we also obtain analytical expressions for the low energy behavior of the eigenvalues and eigenfunctions of a string with rapidly oscillating density, recovering (in a simpler way) results in the literature.     

Intramolecular association within the SAFT framework

A general theory for modelling intramolecular association within the SAFT framework is proposed. Sear and Jackson [Phys. Rev. E. 50 (1), 386 (1994)] and Ghonasgi and Chapman [J. Chem. Phys. 102 (6), 2585 (1995)] have previously extended SAFT to include intramolecular association for chains with two sites. We show that the resulting equations from the two approaches are equivalent, and use their work as a basis for developing a new general theory. The approach used by Ghonasgi and Chapman is based on mass balances and an infinite dilution result and provides the equations needed to determine the contribution to the Helmholtz free energy from association (inter- as well as intramolecularly) at equilibrium. Sear and Jackson rederived the contribution to the Helmholtz free energy from association from the theory by Wertheim [J. Stat. Phys. 42 (3–4), 459 (1986)] with inclusion of intramolecular association, and using this approach we obtain an expression for the Helmholtz free energy that is valid also at non-equilibrium states (with respect to hydrogen bonds), which is very useful when calculating derivatives.     

Surface free energy of platinum nanoparticles at zero pressure: A molecular dynamic study

Metallic nanoparticles are interesting because of their use in catalysis and sensors. The surface energy of the FCC platinum nanoparticles are investigated via molecular dynamics simulation using Quantum Sutton–Chen (QSC) potential. We have calculated the Gibbs free energy for the FCC platinum bulk and also for its nanoparticle. All calculations have been carried out at zero pressure. We have used the thermodynamic integration method to obtain the Gibbs free energy. The total Gibbs free energy is taken as the sum of its central bulk and its surface free energy. We have calculated the free energy of a platinum nanoparticle as a function of temperature.     

Relativistic stellar models

We obtain a class of solutions to the Einstein–Maxwell equations describing charged static spheres. Upon specifying particular forms for one of the gravitational potentials and the electric field intensity, the condition for pressure isotropy is transformed into a hypergeometric equation with two free parameters. For particular parameter values we recover uncharged solutions corresponding to specific neutron star models. We find two charged solutions in terms of elementary functions for particular parameter values. The first charged model is physically reasonable and the metric functions and thermodynamic variables are well behaved. The second charged model admits a negative energy density and violates the energy conditions.