Rigorous Equations Research Articles

Study on spontaneous emission in complex multilayered plasmonic system via surface integral equation approach with layered medium Green’s function

A rigorous surface integral equation approach is proposed to study the spontaneous emission of a quantum emitter embedded in a multilayered plasmonic structure with the presence of arbitrarily shaped metallic nanoscatterers. With the aid of the Fermi's golden rule, the spontaneous emission of the emitter can be calculated from the local density of states, which can be further expressed by the imaginary part of the dyadic Green's function of the whole electromagnetic system. To obtain this Green's function numerically, a surface integral equation is established taking into account the scattering from the metallic nanoscatterers. Particularly, the modeling of the planar multilayered structure is simplified by applying the layered medium Green's function to reduce the computational domain and hence the memory requirement. Regarding the evaluation of Sommerfeld integrals in the layered medium Green's function, the discrete complex image method is adopted to accelerate the evaluation process. This work offers an accurate and efficient simulation tool for analyzing complex multilayered plasmonic system, which is commonly encountered in the design of optical elements and devices.

Asymptotic analysis of nonlinear micro-film buckling

The buckling design of micro-films has various potential applications to engineering. The substrate prestrain, interconnector buckling amplitude and critical strain are important parameters for the buckling design. In the presented analysis, the buckled film shape was described approximately by a trigonometric function and the buckled film amplitude was obtained by minimizing the total strain energy. However, this method only generates the first-order approximate solution for the nonlinear buckling. In the present paper, an asymptotic analysis based on the rigorous nonlinear differential equation for the buckled micro-film deformations is proposed to obtain more accurate relationship of the buckling amplitude and critical strain to prestrain. The obtained results reveal the nonlinear relation and are significant to accurate buckling design of micro-films.

Hierarchical Order Parameters for Macromolecular Assembly Simulations I: Construction and Dynamical Properties of Order Parameters.

Macromolecular assemblies often display a hierarchical organization of macromolecules or their sub-assemblies. To model this, we have formulated a space warping method that enables capturing overall macromolecular structure and dynamics via a set of coarse-grained order parameters (OPs). This article is the first of two describing the construction and computational implementation of an additional class of OPs that has built into them the hierarchical architecture of macromolecular assemblies. To accomplish this, first, the system is divided into subsystems, each of which is described via a representative set of OPs. Then, a global set of variables is constructed from these subsystem-centered OPs to capture overall system organization. Dynamical properties of the resulting OPs are compared to those of our previous nonhierarchical ones, and implied conceptual and computational advantages are discussed for a 100ns, 2 million atom solvated Human Papillomavirus-like particle simulation. In the second article, the hierarchical OPs are shown to enable a multiscale analysis that starts with the N-atom Liouville equation and yields rigorous Langevin equations of stochastic OP dynamics. The latter is demonstrated via a force-field based simulation algorithm that probes key structural transition pathways, simultaneously accounting for all-atom details and overall structure.

Nanosystem Self-Assembly Pathways Discovered via All-Atom Multiscale Analysis

We consider the self-assembly of composite structures from a group of nanocomponents, each consisting of particles within an N-atom system. Self-assembly pathways and rates for nanocomposites are derived via a multiscale analysis of the classical Liouville equation. From a reduced statistical framework, rigorous stochastic equations for population levels of beginning, intermediate, and final aggregates are also derived. It is shown that the definition of an assembly type is a self-consistency criterion that must strike a balance between precision and the need for population levels to be slowly varying relative to the time scale of atomic motion. The deductive multiscale approach is complemented by a qualitative notion of multicomponent association and the ensemble of exact atomic-level configurations consistent with them. In processes such as viral self-assembly from proteins and RNA or DNA, there are many possible intermediates, so that it is usually difficult to predict the most efficient assembly pathway. However, in the current study, rates of assembly of each possible intermediate can be predicted. This avoids the need, as in a phenomenological approach, for recalibration with each new application. The method accounts for the feedback across scales in space and time that is fundamental to nanosystem self-assembly. The theory has applications to bionanostructures, geomaterials, engineered composites, and nanocapsule therapeutic delivery systems.

A knowledge representation model for the optimisation of electricity generation mixes

Energy models such as MARKAL, MESSAGE and DNE-21 are optimisation tools which aid in the formulation of energy policies. The strength of these models lie in their solid theoretical foundations built on rigorous mathematical equations designed to process numerical (quantitative) data related to economics and the environment.Nevertheless, a complete consideration of energy policy issues also requires the consideration of the political and social aspects of energy. These political and social issues are often associated with non-numerical (qualitative) information. To enable the evaluation of these aspects in a computer model, we hypothesise that a different approach to energy model optimisation design is required.A prototype energy model that is based on a semantic representation using ontologies and is integrated to engineering models implemented in Java has been developed. The model provides both quantitative and qualitative evaluation capabilities through the use of logical inference. The semantic representation of energy policy goals is used (i) to translate a set of energy policy goals into a set of logic queries which is then used to determine the preferred electricity generation mix and (ii) to assist in the formulation of a set of equations which is then solved in order to obtain a proposed electricity generation mix.Scenario case studies have been developed and tested on the prototype energy model to determine its capabilities. Knowledge queries were made on the semantic representation to determine an electricity generation mix which fulfilled a set of energy policy goals (e.g. CO2 emissions reduction, water conservation, energy supply security). An optimised electricity generation mix, based on the queried results, was then generated using a custom developed linear programming optimisation module.

Unified cardinalized probability hypothesis density filters for extended targets and unresolved targets

The unified cardinalized probability hypothesis density (CPHD) filters for extended targets and unresolved targets are proposed. The theoretically rigorous measurement-update equations for the proposed filters are derived according to the theory of random finite set (RFS) and finite-set statistics (FISST). By assuming that the predicted distributions of the extended targets and unresolved targets and the distribution of the clutter are Poisson, the exact extended-target and unresolved-target CPHD correctors reduce to the exact extended-target and unresolved-target PHD correctors, respectively. Since the exact CPHD and PHD corrector equations involve with a number of operations that grow exponentially with the number of measurements, the computationally tractable approximations for them are presented, which can be used when the extended targets and the unresolved targets are not too close together and the clutter density is not too large. Monte Carlo simulation results show that the approximate extended-target and unresolved-target CPHD filters, respectively, outperform the approximate extended-target and unresolved-target PHD filters a lot in estimating the target number and states, although the computational requirement of the CPHD filters is more expensive than that of the PHD filters.

WAVE PROPAGATION IN A WAVEGUIDE SECTION WITH SHARP CORRUGATIONS

The rigorous excitation equations are used to analyze wave propagation in a rectangular waveguide section with sharp periodic corrugations whose height is much greater than the period. It has been shown that the Brillouin diagram of the corrugated and regular waveguides in the case of strong gradient scattering is characterized by qualitatively the same frequency dependence of the longitudinal wavenumber. The only difference is that the cutoff frequencies of the corrugated waveguide modes increase with decreasing the corrugation period, and it is always possible to implement the single-mode regime within an arbitrary frequency range lying higher than the first cutoff frequency. The effect can be used to suppress the mode competition in microwave amplifiers, as well as in narrow-band oscillators provided that the latter involve the Bragg reflectors as a feed-back.

0124 柔軟構造体を設置した平行平板間乱流の流動特性(OS1 噴流,後流および剥離流れ現象の探求と技術革新,オーガナイズドセッション)

In the present paper in order to investigate the possibility of flow control using elastic body, we conduct a simulation of a finite-length square cylinder placed inside turbulent channel flow. For an elastic cylinder, the rigorous equation of motion for elastic continuum is solved with a finite volume method; the effect of existence of cylinder in the flow computation is taken into account using the immersed boundary method. From time averaged quantities, we demonstrate that the flow pattern around rigid cylinder is in accordance with that of previous reported experimental results and that the elastic cylinder markedly modulates the wake structure, u

DNS of turbulent flow in a channel with an elastic cantilever

In various scientific fields, numerical solving of fluid-structure interaction (FSI) problems are of importance. Therefore the establishment of stable numerical scheme is needed to analyze the details of flow phenomena. In the present paper, a weak-coupling method for FSI problem is proposed: the rigorous equations of motion for a elastic body are discretized with finite volume method; the elastic body is reproduced via immersed boundary method in the flow computation. In order to demonstrate the performance of proposed scheme, the 3D structure analysis and 3D FSI problems of a elastic body are solved. It is found that the computation is stably conducted using the proposed method, in spite of the occurrence of fairly large deformation of the object. Also it turns out that the realistic flow including turbulence phenomena is well reproduce using the proposed FSI scheme.

Propagation Wavenumbers for Half- and Full-Width Microstrip Lines in the ${ EH}_{1}$ Mode

Equations are presented for calculating the propagation wavenumbers for half- and full-width microstrip lines operating in the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">EH</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> mode. The transverse resonance method is used for determining the propagation wavenumbers. For the half-width microstrip line, only the self-admittance of the open edge needs to be considered. The self-admittance can be calculated from either the rigorous equations or the simplified formulas, both of which have been derived previously using the Wiener-Hopf method. However, for the full-width microstrip line, the mutual admittance between the two open edges of the microstrip line also needs to be considered. For the first time, the mutual admittance is calculated accurately with the spectral-domain immittance method, and approximately with a space-domain method. By accounting for the mutual admittance, the accuracy of the wavenumber of the full-width microstrip line is greatly improved.

Oxygen isotope fractionation in the ocean surface and18O/16O of atmospheric O2

[1] We have recently published a new evaluation of Earth's Dole effect, which was based, in part, on measurements of δO2/Ar, δ17O and δ18O of dissolved argon and oxygen in the ocean surface. In calculations of the oxygen isotope effect due to photosynthesis and respiration (ɛup), gross O2 production (G) was an important factor. However, our estimates of G were based on an approximate equation, and in a recent publication it has been suggested that G obtained with this equation could be underestimated by about 33%. If true, such underestimation of G might lead to different ɛup values. To test this possibility, we have used a new rigorous equation with relevant information on isotopic composition of photosynthetic O2 and recalculated ɛup. Given the uncertainties, the new values do not differ from the previous ones, and therefore, the implications of the strong fractionation in the upper ocean (∼25‰) to the global Dole effect remain as in our original publication.

Theoretical investigation on saturated Förster-Resonant-Energy-Transfer Microscopy using FRET dye pairs as fluorescent probes

Saturated Förster-Resonant-Energy-Transfer (FRET) microscopy (SFM) employing tiny silica nanoparticles densely co-doped with Cy3 and Cy5 molecules as fluorescent labels has been proposed and analyzed with rigorous rate equations previously, showing that optical resolutions beyond the diffraction-limit in both lateral and axial directions can be realized by exploiting the saturation effect in FRET process. Here, using a set of similar rate equations, we show that SFM can also be realized with single FRET dye pairs as fluorescent labels. A similar nonlinear optical response to excitation beam is revealed for Cy3–Cy5 dye pairs, in comparison to the silica nanoparticles co-doped with Cy3 and Cy5 molecules.

Proper estimation of marine gross O2production with17O/16O and18O/16O ratios of dissolved O2

[1] Recently, the method for estimation of marine gross production from measurements of 17O/16O and 18O/16O of dissolved O2 has been improved by obtaining a rigorous equation for evaluation of gross production, and it has been suggested that small errors associated with approximations resulted in significant underestimation of gross production rates. The new equation requires accurate knowledge of the isotopic composition of photosynthetic and atmospheric oxygen. While the values for the latter have been determined very precisely, those of the former have never been measured. Here we present the first experimentally derived values of δ17Op and δ18Op of marine photosynthetic O2 (−10.126 and −20.014 ‰). Based on these, we show that the suggested underestimation was not the result of approximation errors, rather it was caused by inaccurate estimated values of δ17Op and δ18Op.

A Generalized 90° Impedance Transformer with Improved Spurious Suppression for Arbitrary Real Terminated Impedances

A generalized impedance transformer for arbitrary real terminated impedances is proposed in this article. This transformer mainly features 90° phase shifting at the operating frequency, matching for arbitrary real terminated impedances, and improved spurious suppression. It consists of two-section transmission lines and three parallel transmission-line stubs. By equating the ABCD matrixes of the proposed impedance transformer and conventional quarter-wavelength impedance transformer, closed-form design equations are obtained as a final analytical design approach. Several numerical and measured microstrip transformers with improved spurious suppression are presented. Finally, experimental performances verify this generalized structure and the proposed rigorous design equations.

A Hybrid Transport Point-Kinetic method for simulating source transients in subcritical systems

Abstract This paper describes a novel hybrid technique for the solution of the time-dependent neutron transport equation in source switch-on transients. The Hybrid Transport Point Kinetics (HTPK) method is derived from a multi-collision description of the transport equation and is based on the observation that the external source mainly influences the first few neutron generations and, through collisions and multiplications, an ensemble behavior statistically emerges at higher order. The HTPK is designed to separately describe the propagation phenomenon from the ensemble response of the system, using both the rigorous transport equation and simplified kinetic models. Numerical simulations performed on a typical acceleration driven system configuration confirm the basic physical intuition of HTPK and show a significant gain in accuracy when compared to classical point kinetics. The proposed HTPK technique is also shown to be attractive because of its flexibility and competitive computational effort.

Relativistic Doppler effect in an extending transmission line: Application to lightning

We present in this paper a thorough analysis of current wave propagation with arbitrary speed along an extending transmission line. We derive rigorous analytical equations in the time and frequency domains expressing the reflections of the current wave occurring at the extending end of the line. The derived equations reveal that it is not possible to represent current reflections occurring at the extending end of a transmission line using a constant, frequency-independent reflection coefficient, as previously done in the literature. The reflected wave from the extending end of the line is shown to be affected by the Doppler frequency shift. In other words, the reflected wave from an extending transmission line suffers distortion, the amount of which depends on the incident wave form, its frequency content, and the speed of the extending end of the line. The derived expression is in agreement with the relativistic Doppler effect and is consistent with the Lorentz transformation. Finally, engineering models for return strokes are generalized and closed-form analytical expressions are derived for the spatial-temporal distribution of the current along the channel accounting for reflections at ground and at the return stroke wave front taking into account the Doppler effect.

Axial soil–pile interaction in a transversely isotropic half-space

A rigorous integral equation formulation is presented for the axisymmetric load-transfer analysis of a thin-walled pile embedded in a transversely isotropic half-space under axial load. By virtue of a set of ring-load Green’s functions for the pile and one for the half-space, the problem is shown to be reducible to a pair of Fredholm integral equations. Through a mathematical analysis of an auxiliary pair of Cauchy integral equations, the inherent singularities of the contact stress distributions are rendered explicit. With a direct incorporation of the singular nature of the resultant load transfers, the numerical solution of the integral equations is shown to be possible by an interpolation of regular functions only. Typical results for various material and geometrical conditions are presented, including a comparison with past classical solutions, to illustrate the effects of transverse anisotropy on the load-transfer process.

Lorentz-covariant quantum transport and the origin of dark energy

A possible explanation for the enigma of dark energy, responsible for about 76% of the mass–energy of the universe, is obtained by requiring only that the rigorous continuity equation (the Boltzmann transport equation) for quanta propagating through space should have the form of a Lorentz-covariant and dispersion-free wave equation. This requirement implies (i) properties of space–time that an observer would describe as uniform expansion in agreement with Hubble's law and (ii) that the quantum transport behaves like in a multiplicative medium with multiplication factor ν=2. This inherent, essentially explosive multiplicity of vacuum, caused by the requirement of Lorentz covariance, is suggested as a potential origin of dark energy. In addition, it is shown (iii) that this requirement of Lorentz-covariant quantum transport leads to an apparent accelerated expansion of the universe.

Publisher’s Note: Heavy-baryon chiral perturbation theory approach to thermal neutron capture onHe3[Phys. Rev. C83, 034006 (2011)

The cross section for radiative thermal neutron capture on ${}^{3}He$ ($\He3 +n \to \He4 +\gamma$; known as the $hen$ reaction) is calculated based on heavy-baryon chiral perturbation theory. The relevant M1 operators are derived up to next-to-next-to-next-to-leading order (N${}^3$LO). The initial and final nuclear wave functions are obtained from the rigorous Faddeev-Yakubovski equations for five sets of realistic nuclear interactions. Up to N${}^3$LO, the M1 operators contain two low-energy constants, which appear as the coefficients of non-derivative two-nucleon contact terms. After determining these two constants using the experimental values of the magnetic moments of the triton and ${}^3 He$, we carry out a parameter-free calculation of the $hen$ cross section. The results are in good agreement with the data.

Heavy-baryon chiral perturbation theory approach to thermal neutron capture onHe3

The cross section for radiative thermal neutron capture on ${}^{3}\text{He}$ (${}^{3}\text{He}+n\ensuremath{\rightarrow}{}^{4}\text{He}+\ensuremath{\gamma}$; known as the $\mathit{hen}$ reaction) is calculated based on heavy-baryon chiral perturbation theory. The relevant M1 operators are derived up to next-to-next-to-next-to-leading order (N$^{3}\mathrm{L}$O). The initial and final nuclear wave functions are obtained from the rigorous Faddeev-Yakubovski equations for five sets of realistic nuclear interactions. Up to $\mathrm{N}{}^{3}$LO, the M1 operators contain two low-energy constants, which appear as the coefficients of nonderivative two-nucleon contact terms. After determining these two constants using the experimental values of the magnetic moments of the triton and ${}^{3}\text{He}$, we carry out a parameter-free calculation of the $\mathit{hen}$ cross section. The results are in good agreement with the data.