Detection of intensity change points in time-resolved single-molecule measurements

We present a method for the analysis of optical single molecule emission data that exhibit discrete intensity jumps. This new method uses a generalized likelihood ratio test that determines the location of an intensity change point based on individual photon arrival times. This test is applied recursively to an entire single molecule intensity trajectory, thus finding each change points. Expectation-maximization clustering and the Bayesian information criterion is then used for accurate determination of the true number of states accessible to the system. This procedure allows rigorous and quantitative determination of intensity change points without the artificial time resolution limitations that arise from binning and thresholding.     

An algorithm for the location of branching points on reaction paths

A branching point is a point on a reaction path leading from reactants to products (via a transition state) at which it is energetically favorable for the system to break symmetry. Such a point can be defined in terms of normal modes along the reaction path and corresponds to zero curvature (a zero Hessian eigenvalue) along a symmetry-breaking mode. An effective method for the location of such points is presented and realized in an efficient, practical algorithm designed for use in the ab initio program package Gaussian 82.     

Comparison of methods for finding saddle points without knowledge of the final states

Within the harmonic approximation to transition state theory, the biggest challenge involved in finding the mechanism or rate of transitions is the location of the relevant saddle points on the multidimensional potential energy surface. The saddle point search is particularly challenging when the final state of the transition is not specified. In this article we report on a comparison of several methods for locating saddle points under these conditions and compare, in particular, the well-established rational function optimization (RFO) methods using either exact or approximate Hessians with the more recently proposed minimum mode following methods where only the minimum eigenvalue mode is found, either by the dimer or the Lanczos method. A test problem involving transitions in a seven-atom Pt island on a Pt(111) surface using a simple Morse pairwise potential function is used and the number of degrees of freedom varied by varying the number of movable atoms. In the full system, 175 atoms can move so 525 degrees of freedom need to be optimized to find the saddle points. For testing purposes, we have also restricted the number of movable atoms to 7 and 1. Our results indicate that if attempting to make a map of all relevant saddle points for a large system (as would be necessary when simulating the long time scale evolution of a thermal system) the minimum mode following methods are preferred. The minimum mode following methods are also more efficient when searching for the lowest saddle points in a large system, and if the force can be obtained cheaply. However, if only the lowest saddle points are sought and the calculation of the force is expensive but a good approximation for the Hessian at the starting position of the search can be obtained at low cost, then the RFO approaches employing an approximate Hessian represent the preferred choice. For small and medium sized systems where the force is expensive to calculate, the RFO approaches employing an approximate Hessian is also the more efficient, but when the force and Hessian can be obtained cheaply and only the lowest saddle points are sought the RFO approach using an exact Hessian is the better choice. These conclusions have been reached based on a comparison of the total computational effort needed to find the saddle points and the number of saddle points found for each of the methods. The RFO methods do not perform very well with respect to the latter aspect, but starting the searches further away from the initial minimum or using the hybrid RFO version presented here improves this behavior considerably in most cases.     

Energy isosbestic points in third-row transition metal alloys

The total electronic energies of the six electrons per atom (e per atom) alloys W, TaRe, HfOs, and YIr and the seven electrons per atom alloys Re, WOs, TaIr, HfPt, and YAu have been calculated in the local density approximation of density functional theory. When one considers common alloy structures such as atomically ordered variants of the body-centered cubic, face-centered cubic, or hexagonally closest packed structures and plots the total electronic energy as a function of the unit cell parameter, one finds for both the six and seven electrons per atom series energetic isosbestic points. An energetic isosbestic point corresponds to a critical value of the size parameter for which all members of the 6 or 7 e per atom series of compounds have nearly identical total electronic energy. Just as in spectroscopy, where the existence of such isosbestic points is the hallmark of two compounds present in the mixture, an energy isosbestic point implies there are just two separate energy curves. For both series it is found that the total electronic energy can be viewed as the weighted sum of a purely covalent term and a purely ionic term. Two semi-quantitative models are proposed to account for these two separate energies. In the first model the total energy is viewed as the sum of the elemental structural energy plus an ionic energy based on the Born-Mayer ionic model. In the second model one considers within the confines of mu2-Hückel theory the evolution of the total electronic energy as the Coulombic Hii integrals change in value.     

Four points function fitted and first derivative procedure for determining the end points in potentiometric titration curves: statistical analysis and method comparison.

A new method that belongs to the differential category for determining the end points from potentiometric titration curves is presented. It uses a preprocess to find first derivative values by fitting four data points in and around the region of inflection to a non-linear function, and then locate the end point, usually as a maximum or minimum, using an inverse parabolic interpolation procedure that has an analytical solution. The behavior and accuracy of the sigmoid and cumulative non-linear functions used are investigated against three factors. A statistical evaluation of the new method using linear least-squares method validation and multifactor data analysis are covered. The new method is generally applied to symmetrical and unsymmetrical potentiometric titration curves, and the end point is calculated using numerical procedures only. It outperforms the "parent" regular differential method in almost all factors levels and gives accurate results comparable to the true or estimated true end points. Calculated end points from selected experimental titration curves compatible with the equivalence point category of methods, such as Gran or Fortuin, are also compared with the new method.     

Ammonium bisulfate/water: a pseudobinary system

We have studied the ammonium bisulfate/water system using thermal analysis (differential scanning calorimetry) and infrared spectroscopy of thin films. Our results for the melting points for ice and letovicite are in good agreement with other experimental work. However, we report here the first measurements of the ice/ammonium bisulfate/letovicite invariant point. We have used our observations and solubility data to construct a complete phase diagram for this system. Utilizing phase diagram theory and the Gibbs phase rule, we conclude that this system is not a true binary system but rather a pseudobinary system, which has a range of concentrations that cannot be represented by a simple binary phase diagram and thus must be viewed as part of the ternary system: H(2)SO(4)/(NH(4))(2)SO(4)/H(2)O. We also compared our results to the phase diagram predictions of the aerosol inorganics model and found the predicted melting points are in good agreement with experimental work over a limited concentration range, but the transitions predicted by the model at lower temperatures are not in agreement with experimental results.     

Measurements and theoretical interpretation of points of zero charge/potential of BSA protein

The points of zero charge/potential of proteins depend not only on pH but also on how they are measured. They depend also on background salt solution type and concentration. The protein isoelectric point (IEP) is determined by electrokinetical measurements, whereas the isoionic point (IIP) is determined by potentiometric titrations. Here we use potentiometric titration and zeta potential (ζ) measurements at different NaCl concentrations to study systematically the effect of ionic strength on the IEP and IIP of bovine serum albumin (BSA) aqueous solutions. It is found that high ionic strengths produce a shift of both points toward lower (IEP) and higher (IIP) pH values. This result was already reported more than 60 years ago. At that time, the only available theory was the purely electrostatic Debye-Hu?ckel theory. It was not able to predict the opposite trends of IIP and IEP with ionic strength increase. Here, we extend that theory to admit both electrostatic and nonelectrostatic (NES) dispersion interactions. The use of a modified Poisson-Boltzmann equation for a simple model system (a charge regulated spherical colloidal particle in NaCl salt solutions), that includes these ion specific interactions, allows us to explain the opposite trends observed for isoelectric point (zero zeta potential) and isoionic point (zero protein charge) of BSA. At higher concentrations, an excess of the anion (with stronger NES interactions than the cation) is adsorbed at the surface due to an attractive ionic NES potential. This makes the potential relatively more negative. Consequently, the IEP is pushed toward lower pH. But the charge regulation condition means that the surface charge becomes relatively more positive as the surface potential becomes more negative. Consequently, the IIP (measuring charge) shifts toward higher pH as concentration increases, in the opposite direction from the IEP (measuring potential).     

Analysis of a reversible five-point bending configuration based on a novel two-sense support

A novel two-sense support for flexural tests has been designed and manufactured in Ikerlan. The aim of this support is to do two-sense bending fatigue tests. In order to reduce the displacement corresponding to a given stress, a novel test configuration, designated as five-point bending, is modelled analytically. Basically, it is a three-point configuration with two supports at the ends that exert forces in the same sense as the applied load. In this way, a partial clamping is obtained that can be modelled by concentrated loads. The model has been checked carrying out quasi-static three-point and five-point bending tests at different spans in unidirectional carbon/epoxy composite specimens. Flexural modulus and the out-of-plane shear modulus have been obtained by linear regression in both cases, after having obtained experimentally the stiffness of the system.     

Apparatus for the determination of melting points, molecular weights, freezing points and purity, and for the study of melting

An apparatus for the determination of the melting point of a partially frozen liquid is described. Thermal equilibrium is rapidly attained, largely because of the presence of glass balls in the experimental flask, and the method of agitation. The use of a thermistor and a recording potentiometer allows charting of the temperature changes with time. The melting point can be calculated from points on the trace. The apparatus has been used to study melting point depressions for solutions of hydrocarbons and phenols in benzene, nitrobenzene, water and dioxan.     

Determination of isoelectric points of acidic and basic proteins by capillary electrophoresis

The isoelectric point (pI) of a protein is of practical importance in many separation procedures, both analytical and preparative. The pI is defined as the pH where the net charge of the protein is zero. Therefore, by plotting the mobilities of the proteins against pH, the intercept at zero mobility should yield the pI value. Isoelectric points have traditionally been determined by isoelectric focusing. In this paper, the potential of capillary electrophoresis as an alternative technique for the determination of pI values of both acidic and basic proteins was investigated. The problem commonly encountered with adsorption of the positively charged proteins with the unprotonated silanol groups of the fused-silica wall is solved by applying a dynamic coating of a polycationic reagent to the wall. The advantages of this technique of determining the pI values are simplicity, speed and minimal sample requirement.     

Efficient and reliable mixture critical points calculation by global optimization

Multicomponent systems may exhibit several critical points or no critical point at all. Local methods can find only one critical point for a given initial guess. Recently, several global methods have been proposed for finding all the solutions of the problem. In the present work, we propose a gradient-based calculation method using global optimization, with temperature and molar volume as primary variables, and with analytical partial derivatives calculated from a two-parameter cubic equation of state. The Tunneling global optimization method is used for finding all the global minima. The implementation is based on a unique feature of the Tunneling method, which is able to find efficiently and reliably multiple minima at the same level. Several mixtures from binaries to petroleum reservoir fluids are used to test the proposed method. Numerical experiments proved the efficiency and reliability of the Tunneling method for finding all mixture critical points.     

3D-map modelling for the melting points prediction of intumescent flame-retardant coatings

The applicability of 3D map modelling for melting point prediction was studied. The melting points in the ammonium polyphosphate–pentaerythritol–melamine chemical system of intumescent flame-retardant coatings over a wide range of concentrations were collected. The ternary diagram (triangle) of the melting points was plotted and an approximated 3D map was built for the range 205–345°C. The present work contains the thermal data for the observed ternary system and provides a new graphic system for making predictions for intumescent flame-retardant coatings. The applicability of the calculated 3D map for obtaining experimental samples of fire-retardant paints with a low melting point for thin steel constructions was shown.     

Computation of stationary points via a homotopy method

A homotopy method is presented that locates both minimizers and saddle points of energy functions in an efficient manner. In contrast to other methods, it makes possible the exploration of large parts of potential energy surfaces. Along a homotopy path stationary points of odd and even order occur alternately. A path tracing procedure requiring only gradients and at most one evaluation of the Hessian matrix is given. Test results on a model potential and three MINDO/3 potentials are reported. Received: 6 May 1996 / Accepted: 2 April 1998 / Published online: 23 June 1998     

Improvement in the generation of adsorption isotherm data in the elution by characteristic points method--the ECP-slope approach

The elution by characteristic points (ECP) method is a very rapid and precise method for determination of the phase system equilibrium of phase systems in broad solute concentration ranges. Thus, the method is especially suitable for rapid characterization of high efficient separation systems. One important source of error, the effects by the post-loop dispersion, was eliminated in a recent investigation. In this study, the systematic error caused by the selection of the integration starting point at concentration equal to 0 is eliminated. This is done by developing and validating a new procedure for isotherm data generation; the ECP-slope method. The method generates raw slope data of the adsorption isotherm instead of raw adsorption data by integrations as the classical ECP does. Both numerical and experimental data were used for the comparison of the classical ECP approach with the slope-ECP method.     

Relationship between the density of supercritical CO_2 + ethanol binary system and its critical properties

The solvent strength and selectivity of supercritical fluids (SCF) can be greatly enhanced by addition of one or two entrainers into the system. The amount of entrainer added is usually less than 5% (mole fraction). However, even with such slight amount, solubility of organic solutes has been observed to increase by several orders magnitude[1]. Therefore, critical pressure and tem-perature data of these supercritical fluid + cosolvent systems are imperative for the reasonable design of effici…     

Saddle points of index 2 on potential energy surfaces and their role in theoretical reactivity investigations

After a general characterization of second order saddle points two boundary cases are derived and illustrated by examples. The utilization of the classification is pointed out. One type, the virtual saddle point of index 2 (V-SP 2), may be understood as geometrical superposition of two saddles of index 1 (transition structures) which belong to relatively independent processes within the chemical system.     

色谱工作站采样时间的迭代计算

采用迭代计算确定色谱工作站采样时间,建立了连续变速采样的方法。方法具有采样点数少,节省内存空间,数据处理速度快及误差小的优点,可用于恒温及等梯度洗脱分析。     

Enthalpy of dissociation and hydration number of methane hydrate from the Clapeyron equation

The enthalpies of the reactions in which methane hydrate is dissociated to methane vapor and either (1) water, or (2) ice are determined by a new analysis using the Clapeyron equation. The difference in enthalpies of the two reactions is used to infer the hydration number at the quadruple point where hydrate, ice, liquid water, and methane vapor coexist. By appropriate corrections, the hydration number at points removed from the quadruple point is also determined. The most important feature of the new analysis is the direct use of the Clapeyron equation. The method avoids the use of certain simplifying assumptions that have compromised the accuracy of previous analyses in which the Clausius-Clapeyron equation was used. The analysis takes into account the finite volumes of all phases, the non-ideality of the vapor phase, and the solubility of methane in water. The results show that the enthalpy of dissociation and hydration number are constant within experimental error over the entire (hydrate, liquid, vapor) coexistence region. The results are more accurate than but entirely consistent with almost all previous studies.     

Locating saddle points of any index on potential energy surfaces by the generalized gentlest ascent dynamics

The system of ordinary differential equations for the method of the gentlest ascent dynamics (GAD) is tested to determine the saddle points of the potential energy surface of some molecules. The method has been proposed earlier [E and Zhou in Nonlinearity 24:1831 (2011)]. We additionally use the metric of curvilinear internal coordinates. By a number of examples, we explain the possibilities of a GAD curve; it can find the transition state of interest by a gentlest ascent, directly or indirectly, or not. A GAD curve can be a model of a reaction path, if it does not contain a turning point for the energy. We further discuss generalized GAD formulas for the search of saddle points of a higher index. We calculate diverse examples.