Superposition Approximation Research Articles

Detection probability of a low-mass planet for triple lens events: implication of properties of binary-lens superposition

In view of the assumption that any planetary system is likely to be composed of more than one planet, and the multiple planet system with a large mass planet has more chance of detailed follow-up observations, the multiple planet system may be an efficient way to search for sub-Jovian planets. We compare the magnification pattern of the triple lens system with that of a best-fitted binary system composed of a star and a Jovian mass planet, and check the probability in detecting the low-mass secondary planet whose signature will be superposed on that of the primary Jovian mass planet. Detection probabilities of the low-mass planet in the triple lens system are quite similar to the probability in detecting such a low-mass planet in a binary system with a star and only a low-mass planet, which shows that the signature of a low-mass planet can be effectively detected even when it is concurrent with the signature of the more massive planet, implying that the binary superposition approximation works over a relatively broad range of planet mass ratio and separations, and the inaccuracies thereof do not significantly affect the detection probability of the lower mass secondary planet. Since the signature of the Jovian mass planet will be larger and lasts longer, thereby warranting more intensive follow-up observations, the actual detection rate of the low-mass planet in a triple system with a Jovian mass can be significantly higher than that in a binary system with a low-mass planet only. We conclude that it may be worthwhile to develop an efficient algorithm to search for `super-Earth' planets in the paradigm of the triple lens model for high-magnification microlensing events.

Multiparticle reaction noise characteristics

A simple multiparticle reaction model was studied where reactants A react with (a possibly large) stoichiometric coefficient k. Each reaction forms a product molecule P, and every product molecule can be split into k A particles through the back reaction. To study the fluctuations in particle numbers a novel approach has been developed; to be referred to as the Pair approach based Reaction Noise EStimator (PARNES) method. The PARNES method is based on the full Kirkwood superposition approximation implemented at the pair level. Kirkwood's method has been adapted to study stochastic properties of an arbitrary reaction network in a perfectly mixed reaction volume. PARNES works well for large particle numbers. It provides qualitative description when particle numbers are low. The PARNES method can easily augment mean field calculations. Extension of the method beyond the pair approach level is straightforward. Both stationary and non-stationary properties of the model were investigated, and the findings of this work point to two possible scenarios of intracellular noise control. When k is increased, the fluctuations in the number of product molecules become smaller (sub-Poissonian) in a stationary state, and relaxation to a stationary state becomes faster.

Electrostatic interaction between two spherical soft particles at small separations

An approximate analytic expression is given for the potential energy of the electrostatic interaction between two identical spherical soft particles (ion-penetrable porous spheres) in a symmetrical electrolyte solution with the help of Derjaguin's approximation. This method uses accurate analytic expressions for the corresponding interaction energy between two parallel similar soft plates (ion-penetrable membranes) obtained previously (J. Colloid Interface Sci., 350 (2010) 249). Agreement with numerical data (J. Colloid Interface Sci., 36 (1989) 523) is excellent for arbitrary potentials and small particle separations, where the Debye–Hückel linearization approximation and the linear superposition approximation are not allowed.

Self-consistent field method and non-self-consistent field method for calculating the positron lifetime

Many methods are used to calculate the positron lifetime, these methods could be divided into two main types. The first method is atomic superposition approximation method and the second one is the so called energy band calculation method. They are also known as the non-self-consistent field method and self-consistent field method respectively. In this paper, we first introduce the two basic methods and then, we take Si as an example and give our calculation results, these results coincide with our latest experimental results, finally, we discuss the advantages and disadvantages of the two methods.

Exact Analytical Expressions for the Potential of Electrical Double Layer Interactions for a Sphere−Plate System

Exact, closed-form analytical expressions are presented for evaluating the potential energy of electrical double layer (EDL) interactions between a sphere and an infinite flat plate for three different types of interactions: constant potential, constant charge, and an intermediate case as given by the linear superposition approximation (LSA). By taking advantage of the simpler sphere-plate geometry, simplifying assumptions used in the original Derjaguin approximation (DA) for sphere-sphere interaction are avoided, yielding expressions that are more accurate and applicable over the full range of κa. These analytical expressions are significant improvements over the existing equations in the literature that are valid only for large κa because the new equations facilitate the modeling of EDL interactions between nanoscale particles and surfaces over a wide range of ionic strength.

Effective Forces in Square Well and Square Shoulder Fluids

We derive an analytical expression for the effective force between a pair of macrospheres immersed in a sea of microspheres, in the case where the interaction between the two unlike species is assumed to be a square well or a square shoulder of given range and depth (or height). This formula extends a similar one developed in the case of hard core interactions only. Qualitative features of such effective force and the resulting phase diagrams are then analyzed in the limit of no interaction between the small particles. Approximate force profiles are then obtained by means of integral equation theories (PY and HNC) combined with the superposition approximation and compared with exact ones from direct Monte Carlo simulations.

Relationship between positron bulk lifetime and lattice constants–research on NaCl-type crystals

The positron lifetimes of some compounds with NaCl-type crystal structure are calculated with the method of atomic superposition approximation (ATSUP) based on the theories of local-density-approximation (LDA) and general-gradient-approximation (GGA). The systematical results are fitted to a curve as a function of lattice constants. The positron bulk lifetimes of some other compounds with NaCl-type crystal structure, which are deduced from the systematical results, are in agreement with the experimental results given in other literature.

A multiscale maximum entropy moment closure for locally regulated space–time point process models of population dynamics

The prevalence of structure in biological populations challenges fundamental assumptions at the heart of continuum models of population dynamics based only on mean densities (local or global). Individual-based models (IBMs) were introduced during the last decade in an attempt to overcome this limitation by following explicitly each individual in the population. Although the IBM approach has been quite useful, the capability to follow each individual usually comes at the expense of analytical tract ability, which limits the generality of the statements that can be made. For the specific case of spatial structure in populations of sessile (and identical) organisms, space-time point processes with local regulation seem to cover the middle ground between analytical tract ability and a higher degree of biological realism. This approach has shown that simplified representations of fecundity, local dispersal and density-dependent mortality weighted by the local competitive environment are sufficient to generate spatial patterns that mimic field observations. Continuum approximations of these stochastic processes try to distill their fundamental properties, and they keep track of not only mean densities, but also higher order spatial correlations. However, due to the non-linearities involved they result in infinite hierarchies of moment equations. This leads to the problem of finding a 'moment closure'; that is, an appropriate order of (lower order) truncation, together with a method of expressing the highest order density not explicitly modelled in the truncated hierarchy in terms of the lower order densities. We use the principle of constrained maximum entropy to derive a closure relationship for truncation at second order using normalisation and the product densities of first and second orders as constraints, and apply it to one such hierarchy. The resulting 'maxent' closure is similar to the Kirkwood superposition approximation, or 'power-3' closure, but it is complemented with previously unknown correction terms that depend mainly on the avoidance function of an associated Poisson point process over the region for which third order correlations are irreducible. This domain of irreducible triplet correlations is found from an integral equation associated with the normalisation constraint. This also serves the purpose of a validation check, since a single, non-trivial domain can only be found if the assumptions of the closure are consistent with the predictions of the hierarchy. Comparisons between simulations of the point process, alternative heuristic closures, and the maxent closure show significant improvements in the ability of the truncated hierarchy to predict equilibrium values for mildly aggregated spatial patterns. However, the maxent closure performs comparatively poorly in segregated ones. Although the closure is applied in the context of point processes, the method does not require fixed locations to be valid, and can in principle be applied to problems where the particles move, provided that their correlation functions are stationary in space and time.

COMPARING THE ENERGY SPECTRA OF ULTRAHIGH ENERGY COSMIC RAYS MEASURED WITH EXTENSIVE AIR SHOWER ARRAYS

The energy spectra of ultra-high energy cosmic rays (CRs) measured with giant extensive air shower (EAS) arrays exhibit discrepancies between the flux intensities and/or estimated CR energies exceeding experimental errors. The well-known intensity correction factor due to the dispersion of the measured quantity in the presence of a rapidly falling energy spectrum is insufficient to explain the divergence. Another source of systematic energy determination error is proposed concerning the charged particle density measured with the surface arrays, which arises due to simplifications (namely, the superposition approximation) in nucleus-nucleus interaction description applied to the shower modeling. Making use of the essential correction factors results in congruous CR energy spectra within experimental errors. Residual differences in the energy scales of giant arrays can be attributed to the actual overall accuracy of the EAS detection technique used. CR acceleration and propagation model simulations using the dip and ankle scenarios of the transition from galactic to extragalactic CR components are in agreement with the combined energy spectrum observed with EAS arrays.

Interaction between like-charged particles at a liquid interface: Electrostatic repulsion vs. electrocapillary attraction

The electric field of charged particles, which are adsorbed at a liquid interface, induces interfacial deformations (capillary menisci). The overlap of such deformations gives rise to electrocapillary force of interaction between the particles. Our goal is to quantify this interaction on the basis of a force approach, which is different from the approaches (mostly based on energy calculations) used by other authors. The fact that the electric field of adsorbed particles has a dipolar asymptotics (due to the image-charge effect) is utilized to derive an analytical expression for the meniscus profile. The comparison of the calculated profile with experimental data indicates that the results based on the dipolar approximation agree excellently with the data, except some small deviations near the contact line. The effect of the interfacial deformation on the electrostatic pressure is also taken into account. The two-particle electrocapillary problem is solved in bipolar coordinates without using the superposition approximation. It turns out that for uniform distribution of the surface charges, the electrocapillary attraction is weaker than the electrostatic repulsion at interparticle distances at which the dipolar approximation is applicable, so that the net force is repulsive. This result is in agreement with the conclusions of other authors obtained by using different theoretical approaches and with available experimental data. The analytical expressions for the electrocapillary and electrodipping forces derived in the present article provide a simple and convenient way for estimation of these forces.

Calculation of positron bulk lifetime of sphalerite crystalloid

Here, we calculated theoretically the positron bulk lifetime of cuprous halide (except CuI,which has not the blende structure) and some borides with the method of atomic superposition approximation (ATSUP) on the basis of the theory of local density approximation (LDA) and general gradient approximation (GGA),the calculated results are in good agreement with the experiment. On the other hand, the positron lifetime of many other compounds which have blende structure are calcualted,and the results agree with the results published in literatur. Here we take the CuCl as an example,the pictures of the electron potential energy distribution, probability density of positron and positron annihilation rate are given. Finally the systematic results were fitted with curve as a function of lattice constants, and the fitted results are compared with the outcomes of other articles.

Comprehensive Analysis on the Structure and Proton Switch in H+(CH3OH)m(H2O)n (m + n = 5 and 6)

Theoretical and experimental methods were integrated to investigate the structures of H(+)(CH(3)OH)(m)(H(2)O)(n) clusters for m + n = 5 and 6. An effective theoretical approach is presented to search for extensive sets of structural isomers using an empirical model and substitution schemes. Stable isomers were then reoptimized by the B3LYP level of computations with the 6-31+G* basis set. Canonical averages of these structural isomers were analyzed by harmonic superposition approximation (HSA) to study their finite temperature behavior and enable quantitative comparisons with experimental results. Thermal energy is found to have a significant effect on the structure of these clusters. Our calculations show that cyclic isomers are preferred at low temperature, while linear and tree forms become more favorable at high temperature (>200 K). Furthermore, we found that proton can reside on both water and methanol ion cores and the proton switch is associated with morphology change. Experimental IR spectra in the free OH stretching region were also obtained and compared with calculated spectra.

A Hierarchical Approach to Study the Thermal Behavior of Protonated Water Clusters H(+)(H2O)n.

The energy landscape of protonated water clusters H(+)(H2O)n is thoroughly explored at the first-principle level using a hierarchical search methodology. In particular, the distinct configurational isomers of OSS2 empirical potential for n = 5-9 are uncovered and archived systematically using an asynchronous genetic algorithm and are subsequently refined with first-principle calculations. Using the OSS2 model, quantitative agreements in the thermal properties between Monte Carlo and harmonic superposition approximation (HSA) highlighted the reliability of the latter approach for the study of small- to medium-sized protonated water clusters. From the large sets of collected isomers, finite temperature behavior of the clusters can be efficiently examined at first-principle accuracy with the use of HSA. From the results obtained, evidence of structural changes from single-ring to treelike (n = 5-7) and multi-ring to single-ring structures (n = 7-9) is observed, as expected for the empirical model. Finally, the relevance of these findings to recent experimental data is discussed.

Quantum densities of states of fluxional polyatomic systems from a superposition approximation

The superposition method is used to calculate quantum densities of states of polyatomic systems with multiple isomeric structures. For each isomer, anharmonicities are included rigorously using a Dunham expansion of the vibrational energy levels and short exchange Monte Carlo simulations are used to compute the individual quantum densities of states. The method is applied to the computation of thermodynamical properties of the Ar(13) and Ne(13) clusters. The canonical heat capacities are found in very satisfactory agreement with the predictions of quantum or semiclassical sampling methods.

Three-Dimensional Density Profiles of Small and Medium Spheres near a Pair of Large Spheres: Relevance to Entropic Interaction Induced between Large Spheres

In the system we consider, a pair of large hard spheres, whose surface separation is fixed at a prescribed value, is immersed in a binary mixture comprising small and medium hard spheres. The density profiles of the medium and small spheres near the large spheres are calculated using the three-dimensional integral equation theory. When the surface separation equals the medium-sphere diameter, a medium sphere is held between the large spheres in contact with both of their surfaces. This is represented by an extremely sharp, high peak in the reduced density profile of medium spheres. It is found that the profile can be reproduced by the Kirkwood superposition approximation using the reduced density profile of medium spheres around a single large sphere, which is calculated using the radial-symmetric integral equation theory. The small spheres are excluded by the medium sphere held as described above, and the thermal pressure due to the small spheres acting on each large-sphere surface becomes highly asymmet...

Sampling conformations in high dimensions using low-dimensional distribution functions.

We present an approximation to a molecule's N-dimensional conformational probability density function (pdf) in terms of marginal pdfs of highest order l, where l is much less than N. The approximation is constructed as a product of conditional pdfs derived by recursive application of the generalized Kirkwood superposition approximation. Furthermore, an algorithm is presented to sample conformations from the approximate full-dimensional pdf based upon all input marginal pdfs. The sampling algorithm is tested for three small molecule systems by using the algorithm to sample conformations at levels l=1, 2, or 3 and comparing the distributions of sampled conformations with those from the molecular dynamics (MD) simulations. The distributions of conformations sampled at third (l=3) order resemble the MD distributions rather well and significantly better than those sampled at second (l=2) or first (l=1) order. In addition to highlighting the importance of correlations among internal degrees of freedom, these results suggest that low-order correlations suffice to describe most of the conformational fluctuations of molecules in a thermal environment.

The intensity of collision-induced wings of isotropic Raman scattering

The integral intensity of collision-induced wings of isotropic Raman scattering for totally-symmetric vibration has been discussed analytically. The intensity of scattered radiation was considered in the dipole-induced dipole (DID) approach. The radial as well as angular–radial contributions to intensity of scattered radiation were taken into account. Three body radial contribution to integral intensity was evaluated in the Kirkwood superposition approximation. For angular–radial terms we apply B. Ladanyi and T. Keyes' [Mol. Phys., 33 (1977) 1063] approximation, disregarding the “irreducible connected” terms in our formulas describing the integral intensity. For numerical evaluations the Molecular Dynamics (MD) results for the gl 1 l 2 m( r 12) coefficients of the two-body correlation function were used. Analytical formulae were applied numerically to N 2 and CO 2 systems.

Dusty-Plasma Liquid in the Statistical Theory of the Liquid State

Measurements in dusty plasmas were carried out to find the region of validity of approximate relation in statistical theory of liquid states. The integral equations with the Percus-Yewick and the hypernetted-chain closures as well as the superposition approximation were chosen as the objects for investigation. The range of validity of these approaches was obtained by the use of experimental methods for analysis of spatial correlation of dust particles in plasma.

Structure, stability, and infrared spectroscopy of (H2O)nNH4+ clusters: A theoretical study at zero and finite temperature

The combined effects of size and temperature on the stable structures of water clusters doped with one ammonium molecule have been investigated theoretically using an empirical potential and density-functional theory (DFT) calculations. Global optimization with Monte Carlo methods has been performed using an explicit intermolecular potential based on the Kozack-Jordan polarizable model. Putative lowest-energy structures based on this empirical potential are reported. Our results indicate a high propensity for the NH(4)(+) impurity to be fully solvated by water molecules. Clathratelike patterns are formed for clusters containing more than 11 molecules. Local reoptimizations of candidate structures carried out at the DFT level with the B3LYP hybrid functional and the 6-311++G(d,p) basis set confirm the general trends obtained with the intermolecular potential. However, some reorderings between isomers often due to zero-point energy corrections are found in small clusters, leading to stable geometries in agreement with other first-principles studies. Temperature effects have been assessed using a simple harmonic superposition approximation for selected cluster sizes and using dedicated Monte Carlo simulations for (H(2)O)(20)NH(4)(+). The clusters are found to melt near 200 K, and possibly isomerize already below 50 K. The free energy barrier for core/surface isomerization of the impurity in the 21-molecule cluster is estimated to be only a few kcal/mol at 150 K. The vibrational spectroscopic signatures of the clusters obtained from the electronic structure calculations show the usual four O-H stretching bands. As the cluster size increases, the double acceptor-single donor band near 3700 cm(-1) increasingly dominates over the three other bands. While we do not find conclusive evidence for a O-H stretching spectroscopic signature of the ammonium impurity to be in the core or at the surface in the 20-molecule cluster, a possible signature via the N-H stretching bands is suggested near 2800-2900 cm(-1). In the larger (H(2)O)(49)NH(4)(+) cluster, the impurity is slightly more stable at the surface.

Molecular dynamics study on the influence of quencher concentration on the reaction rate for ionic systems

The influence of concentrations of reagents on the rate of reaction: A+B-->C+B for low density equimolar mixtures of spherically symmetric ions immersed in the Brownian medium has been investigated by performing large scale molecular dynamics simulations. The Coulomb potential of ion-ion interactions is truncated at the cutoff distance large enough to make the kinetics of the reaction independent of its value. The simulations have been performed at conditions close to that for quenching reactions for fluophores. One of the simulation results is that the excess in the rate coefficient Delta k is always positive and converges to a constant value which is two to three orders in magnitude higher than that for the soft spheres immersed in the Brownian medium [Litniewski, J. Chem. Phys. 124, 114502 (2006)]. Delta k is approximately proportional to c however, if the concentration is high, positive deviations [O(c(2))] are noticeable. The simulation results are compared with simple model that bases on the superposition approximation. The model predicts most of the properties of Delta k. The predicted values are about 30%-40% lower than that from the simulations.