Application of the mutual-interaction method to a class of two-scatterer systems: I. Two discrete scatterers

Abstract

In a recent paper we developed a formalism that fully accommodates the mutual interactions among scatterers separable by parallel planes. The total fields propagating away from these planes are the unknowns of a system of difference equations. Each scatterer is characterized by a scattering function that expresses the scattered wave amplitude as a function of the incident and scattered wavevectors for a unit-amplitude plane wave scattered from the object in isolation. This function can be derived completely from the scattered far field with the help of analytic continuation. For a two-scatterer system the mutual-interaction equations reduce to a single Fredholm integral equation of the second kind. It turns out that analytic solutions are tractable for those scattering functions that are Dirac deltas or a sum of products of separable functions of the incident and scattered wavevectors. Scattering functions for planes and isotropic scatterers, as well as electric and magnetic dipoles all possess this property and are considered. The exact scattering functions agree with results obtained by analytic continuation. This paper consists of two parts. Part I derives analytic solutions for two discrete scatterers (isotropic scatterers. electric dipoles, magnetic dipoles). Part II is devoted to scattering from an object (isotropic or dipole scatterer) near an interface separating two semi-infinite uniforn-media. Because the results in this paper are exact, the effects of near-field interactions can be assessed. The forms of the scattering solutions can be adapted to objects that are both radiating and scattering.     

金属纳米锥表面吸附分子分布的数值模拟

在均匀外电场中,将吸附在由过渡金属基底生长的纳米锥颗粒表面的CO分子等效为偶极子,在考虑偶极子与局域电场,偶极子之间色散力及偶极子与锥表面原子之间三种相互作用的情况下,给出各相互作用能的数学模型,并用Monte Carlo方法进行数值模拟,得到纳米锥颗粒表面吸附CO分子的空间分布构型.结果表明,在这些相互作用下,纳米锥表面吸附CO分子产生局部凝聚,且随着纳米锥角的变小,吸附在锥顶部的分子更加密集,导致吸附分子间相互作用更强,为解释纳米结构表面吸附体系的异常红外效应提供依据.     

Application of the mutual-interaction method to a class of two-scatterer systems: I. Two discrete scatterers

In a recent paper we developed a formalism that fully accommodates the mutual interactions among scatterers separable by parallel planes. The total fields propagating away from these planes are the unknowns of a system of difference equations. Each scatterer is characterized by a scattering function that expresses the scattered wave amplitude as a function of the incident and scattered wavevectors for a unit-amplitude plane wave scattered from the object in isolation. This function can be derived completely from the scattered far field with the help of analytic continuation. For a two-scatterer system the mutual-interaction equations reduce to a single Fredholm integral equation of the second kind. It turns out that analytic solutions are tractable for those scattering functions that are Dirac deltas or a sum of products of separable functions of the incident and scattered wavevectors. Scattering functions for planes and isotropic scatterers, as well as electric and magnetic dipoles all possess this property and are considered. The exact scattering functions agree with results obtained by analytic continuation. This paper consists of two parts. Part I derives analytic solutions for two discrete scatterers (isotropic scatterers. electric dipoles, magnetic dipoles). Part II is devoted to scattering from an object (isotropic or dipole scatterer) near an interface separating two semi-infinite uniforn-media. Because the results in this paper are exact, the effects of near-field interactions can be assessed. The forms of the scattering solutions can be adapted to objects that are both radiating and scattering.     

The equivalent potential of water molecules for electronic structure of alanine

Using ab initio calculations based on density functional theory, an equivalent potential of water molecules for the electronic structure of Ala in solution has been obtained. The calculation process consists of three steps: first, the geometric structure of Ala + nH₂O system is determined by searching for the lowest energy of the system using free cluster calculation method. Second, based on the geometric structure obtained, the electronic structure of Ala with the potential of water molecules is calculated using a self-consistent cluster-embedding method. Finally, after replacing water molecules with dipoles, the electronic structure of Ala with the potential of dipoles is calculated. The dipoles are adjusted so the electronic structure of Ala with the potential of dipoles is close to that of water molecules. The calculated results show that the main effect of water molecules is to raise the state for methyl CH₃ by about 0.14 Ry, raising all other eigenvalues by about 0.059 Ry, and widening the energy gap by about 25%. In contrast, the replacement of water molecules by dipoles is comparatively efficient, showing that the effect of water molecules on the electronic structure of Ala can be simulated by a dipole potential, which would be a shortcut calculation.     

Application of the mutual-interaction method to a class of two-scatterer systems: II. Scatterer near an interface

Abstract

This paper applies the methodology developed in Part I to the problem of a separable scatterer near a dielectric (penetrable) or perfectly conducting (impenetrable) interface. For a penetrable interface, the scatterer may be on either side of the interface (exposed or embedded). As in Part I, the scatterer may also be an active element. Thus, our solutions extend the classic treatments of dipoles radiating near a planar dielectric interface. The mutual-interaction method accommodates a uniform half-space as an equivalent scattering plate of zero thickness that preserves amplitudes and phases of the transmitted and reflected waves. Because this scattering function necessarily includes a Dirac delta function, exact analytic solutions are possible for the class of separable scatterers, which include isotropic scatterers and electric or magnetic dipoles. The results can be interpreted within the context of image theory. Integrals similar to those derived by Sommerfeld must be evaluated to calculate the spatial fields for dielectric media; however, for highly conducting media good approximations are readily obtained.     

Extremely small domain in the lattice of magnetic dipoles

Lattices of magnetic dipoles with 1–4 rows are investigated. Numerical analysis reveals the smallest stationary domains formed in the lattices, necessary conditions for the formation and destruction of such domains are obtained, and the change in the magnetic moment of the lattices during domain formation is considered. It is shown that the action of an external field on one of the dipoles forming a domain is sufficient for its breaking. The lattices in which the orientational phase transition appears upon perturbation of several dipoles and propagates over the entire system are revealed.     

Mathematical Modeling of the Magnetization of a Two-Dimensional System of Magnetic Moments

Using a system that reaches its minimum energy of interaction at equilibrium, the magnetization of a discrete two-dimensional system of interacting magnetic dipoles by an external magnetic field is modeled mathematically. Magnetization curves for rectangular two-dimensional clusters of dipoles and the region of the magnetic domain are calculated.     

Monte Carlo simulation of Hamaker nanospheres coated with dipolar particles

Parallel tempering Monte Carlo simulation is carried out in systems of N attractive Hamaker spheres dressed with n dipolar particles, able to move on the surface of the spheres. Different cluster configurations emerge for given values of the control parameters. Energy per sphere, pair distribution functions of spheres and dipoles as function of temperature, density, external electric field, and/or the angular orientation of dipoles are used to analyse the state of aggregation of the system. As a consequence of the non-central interaction, the model predicts complex structures like self-assembly of spheres by a double crown of dipoles. This interesting result could be of help in understanding some recent experiments in colloidal science and biology.     

Ground-state properties of a one-dimensional system of dipoles

A one-dimensional (1D) Bose system with dipole-dipole repulsion is studied at zero temperature by means of a quantum Monte Carlo method. It is shown that, in the limit of small linear density, the bosonic system of dipole moments acquires many properties of a system of noninteracting fermions. At larger linear densities, a variational Monte Carlo calculation suggests a crossover from a liquidlike to a solidlike state. The system is superfluid on the liquidlike side of the crossover and is normal deep on the solidlike side. Energy and structural functions are presented for a wide range of densities. Possible realizations of the model are 1D Bose atomic systems, with permanent dipoles or dipoles induced by static field or resonance radiation; or indirect excitons in coupled quantum wires; etc. We propose parameters of a possible experiment and discuss manifestations of the zero-temperature quantum crossover.     

Interbilayer repulsion in nonionic surfactant-water lamellar phases.

We report a simulation study using the RIB modification of the Gibbs' ensemble, for a model membrane system in which the surfaces have embedded dipoles, and are separated by a fluid of discrete TIPS2 water molecules. The separation between the layers is allowed to vary, as is the number of water molecules in the membrane which is in equilibrium with a vapour phase, the whole system being kept at constant (N, V, T). The simulations were performed at 298 K and two systems were studied: in the first, the surface dipoles were modelled as OH groups attached to hydrocarbon chains; in the second, the charge on the O and H atoms was arbitrarily doubled to 0·734 e. The structure of the water around the surface dipoles was examined by collecting density and orientational distributions for different regions in the plane of the surface and for molecularly thick layers of water. Although local water structure is modified by the surface charges, this did not result in a stable bilayer for either of the two dipole strengths. The study has relevance to the stability of nonionic surfactants and phospholipids, and suggests that a factor additional to surface charge is needed to explain the stable structures observed experimentally.     

一种消色差等时性强流束三磁铁偏转系统

 描述了一种由三块二极磁铁组成,无四极透镜的消色差等时性磁偏转系统及其设计方法。根据该系统有关色差性和时差性的关系式与TRACE 3D程序,设计了一个40MeV 、200A电子束的135°偏转系统,该系统显示了良好的消色差性和等时性。     

Application of the mutual-interaction method to a class of two-scatterer systems: II. Scatterer near an interface

This paper applies the methodology developed in Part I to the problem of a separable scatterer near a dielectric (penetrable) or perfectly conducting (impenetrable) interface. For a penetrable interface, the scatterer may be on either side of the interface (exposed or embedded). As in Part I, the scatterer may also be an active element. Thus, our solutions extend the classic treatments of dipoles radiating near a planar dielectric interface. The mutual-interaction method accommodates a uniform half-space as an equivalent scattering plate of zero thickness that preserves amplitudes and phases of the transmitted and reflected waves. Because this scattering function necessarily includes a Dirac delta function, exact analytic solutions are possible for the class of separable scatterers, which include isotropic scatterers and electric or magnetic dipoles. The results can be interpreted within the context of image theory. Integrals similar to those derived by Sommerfeld must be evaluated to calculate the spatial fields for dielectric media; however, for highly conducting media good approximations are readily obtained.     

Acceleration of magnetic dipoles by a sequence of current-carrying turns

Magnetic dipoles are accelerated by a running gradient of the magnetic field that is produced by sequentially energizing current-carrying turns. Magnetic dipoles d _sh = 60 mm in diameter and l _tot = 1 m in length are gasdynamically preaccelerated to velocity V _in = 1 km/s, with which they are injected into the main accelerator. The turnover of the dipoles in the field of an accelerating pulse is prevented and focusing of dipoles is provided by directing the dipoles into a titanium tube. The weight of the dipoles is m = 2 kg, and they acquire final velocity V _fin = 5 km/s over acceleration length L _acc = 300 m.     

Solubility of free and associated strontium in NaCl crystals

The solubility of free and associated strontium in NaCl crystals is investigated by the method of electrical conductivity and ionic thermoconductivity (I.T.C.). The solubility of free strontium in NaCl is rather low, the enthalpy of solution is $\text{h}{}_{\mathrm{d}}{}^{\mathrm{<mtext>f.i.</mtext>}}\text{2}\text{= 0.904}\text{eV}$. The dissolution of segregated strontium in the NaCl lattice is a two-stage process: in the first stage (290–530 K) there are present the isolated I.V. dipoles (peak at 226 K) and Suzuki phase inclusions (peak at 233 K); at ageing temperatures over ～ 530 K there takes place the thermal decomposition of Suzuki phase inclusions: this is the second stage. The solubility of associated strontium is characterized by the energy of solution 0.49 ± 0.03 eV. The reorientation of I.V. dipoles is described by the relaxation mode with τ₀ ～ 10^?13 sec and the enthalpy of 0.66 ± 0.02 eV.     

Physical model and the associative memory of a cytoskeleton microtubule as a system of dipoles

A physical model of the conformational degrees of freedom of a cytoskeleton microtubule represented as a system of interacting dipoles is elaborated, characteristic physical quantities are estimated, and a phase diagram of the ferroelectric state of the microtubule at T = 0 is constructed. The presence of frustrated couplings J _ij between the dipoles appears to be the most important feature of the disordered dipole system of the microtubule, owing to which the ground state of the dipole system splits into a large number of lower energy states. The dynamics of the dipole system is determined by the relaxation of the dipole-dipole interaction energy. After the dipole system has evolved to its final state, the input image is associated with one of reference images stored earlier; hence, the dipole system of a microtubule can be viewed as a distributed system with associative memory.     

Probability distribution function of dipolar field in two-dimensional spin ensemble

We theoretically determine the probability distribution function of the net field of the random planar structure of dipoles which represent polarized particles. At small surface concentrations c of the point dipoles this distribution is expressed in terms of special functions. At the surface concentrations of the dipoles as high as 0.6 the dipolar field obey the Gaussian law. To obtain the distribution function within transitional region c < 0.6, we propose the method based on the cumulant expansion. We calculate the parameters of the distributions for some specific configurations of the dipoles. The distribution functions of the ordered ensembles of the dipoles at the low and moderate surface concentrations have asymmetric shape with respect to distribution medians. The distribution functions allow to calculate various physical parameters of two-dimensional interacting nanoparticle ensembles.     

Generation of disclination dipoles and nanoscopic cracks in deformed nanoceramic materials

The processes of generation of disclination dipoles and nanoscopic cracks (nanocracks) in deformed nanoceramic materials are investigated theoretically. It is demonstrated that disclination dipoles are formed at grain boundaries in the course of grain-boundary sliding. The geometric features of the generation of disclination dipoles are analyzed. The conditions under which the nucleation of nanocracks in the vicinity of the disclination dipoles is energetically favorable are calculated for the nanoceramic materials α-Al₂O₃ (corundum) and 3C-SiC (the cubic phase of silicon carbide). The equilibrium lengths of these nanocracks are also calculated. It is shown that the equilibrium lengths of nanocracks can be comparable to the grain size. As a consequence, these nanocracks can coalesce, thus eventually resulting in the brittle fracture of nanoceramic materials.     

Response of a magnetic nanoparticle lattice to a magnetic field pulse near the stability boundary

The dynamic response of a system being near the stable equilibrium boundary to an external magnetic field pulse is studied for 2D lattices of magnetic nanoparticles with cubic crystallographic anisotropy. The conditions under which magnetic moment oscillations from individual dipoles propagate to the entire system are revealed. This effect results in the lattice response are significantly larger in the external pulse duration and with an amplitude rather weakly depending on initial conditions and external field parameters, the processes during which the pulse results in reorientation of only individual lattice dipoles.     

Effect of dipole-dipole intermolecular forces in the vibration spectra of organic compounds

The potential energy of a polar liquid is derived from the electrostatic interaction of point dipoles, taking into account the formation of local groups with short-range order with minimum energy. The methods of classical mechanics are used to estimate the effects of interaction on the normal vibration frequencies. It is shown that interaction increases the frequencies of low-frequency dipole-rotation vibrations; frequencies of other types may increase or decrease.I am indebted to Professor N. A. Prilezhaeva for discussing these results.     

Nature of the short-range interaction between noble gas atoms and metal surfaces

I propose that an interpretation of the interaction of noble gas atoms with metal surfaces as predominantly physisorbing provides the best explanation for the systematics of their binding energies and surface dipoles, as well as for the tendency of noble gas atoms to bind in low coordinated sites. In the present context physisorption is defined as a process driven by the overlap of the electrostatic atomic potentials of the interacting species. PACS 68.43.Fg; 68.47.De