Rigorous Theoretical Model Research Articles

Controlled Modification of Erbium Lifetime in Silicon Dioxide Film with Chromium or Titanium Coatings

ABSTRACTWe report systematic measurements of the lifetime of the 1.54 μm transition of erbium implanted at different energies in SiO2films coated with titanium or chromium. The lifetime shows a strong reduction up to a factor of 20 with decreasing distance between the erbium and the metal coating. Our experiments combined with rigorous theoretical modeling demonstrate that a high degree of control over the radiative properties of erbium can be achieved in erbium-implanted materials.

Oblique Plane-Wave Scattering From a General Bi-Isotropic Cylindrical Shell With an Interior Advanced Composite-Material Backing

This paper presents a rigorous and efficient theoretical model for analyzing the oblique plane-wave scattering properties of a multilayered bi-isotropic cylindrical shell backed by an interior advanced composite material. The backing material considered is a graphite-fiber-reinforced plastic composite (GFRPC), which is treated as a laminated electrically anisotropic medium. In this model, a recursive eigenfunction theory is derived for describing the electromagnetic fields in the bi-isotropic layers of the cylinder, while a state-equation approach is employed for governing the fields in the anisotropic layers of the cylinder. On the basis of this model, echo widths were computed and, wherever possible, were compared with data available in the literature to validate this model. Particularly, the distinct scattering properties of obliquely incident cases are observed and discussed in detail

Novel attenuation-counter-propagating phase modulator for highly linear fiber-optic links

A key to the development of a high-dynamic-range phase-modulation fiber-optic link is a novel integrated photonic-phase-locked-loop (PPLL) linear phase demodulator, which consists of an inloop phase modulator and feedback control. At present, the propagation delay of the inloop phase modulator is the principal bottleneck in the implementation of this device. This paper specifically concerns a novel attenuation-counter-propagating (ACP) phase modulator (PM) that is free of propagation delay and therefore provides the solution. A rigorous theoretical model and an experimental verification of the ACP phase modulator were provided

Simulations of light scattering spectra of a nanoshell on plane interface based on the discrete sources method

The resonance properties of nanoshells are of great interest in nanosensing applications such as surface enhanced Raman scattering or biological sensing. In this paper the discrete sources method has been applied to analyze the spectrum of evanescent light scattering from a nanoshell particle deposited near a plane surface. Based on the rigorous theoretical model, which allows to take into account all features of the scattering problem as: medium with frequency dispersion, presence of the interface, the objective aperture and its location and core-shell asphericity, the scattering spectrum of nanoshells was calculated. The dependence of the local nanoshell spectral density behavior on its properties is discussed.

Smith-Purcell radiation from a charge moving above a finite-length grating

Smith-Purcell radiation (SPR), generated by an electron beam traveling above a grating, is characterized by a broad range of frequencies. The radiated wavelength depends on the angle of observation according to the SPR resonance relationship and the bandwidth is inversely proportional to the number of the grating grooves. A rigorous theoretical model of SPR from a three-dimensional bunch of relativistic electrons passing above a grating of finite length is presented by an electric-field integral equation method. The finite-length grating results are compared with the case of an infinitely long grating assumption in which periodic boundary conditions are rigorously applied and with a model based on the image-charge approximation. The SPR resonance relationship is the same in all three formalisms. Significant errors in the strength of the radiated energy are introduced by the two approximations. In particular, for gratings with less than $\ensuremath{\sim}20$ periods, the image-charge approximation and the infinitely long grating assumption result in an order of magnitude too high and too low radiated energy per groove, respectively, in the plane transverse to the grating groove lines. Numerical examples are calculated for an $\ensuremath{\sim}18\text{ }\text{ }\mathrm{MeV}$ bunch traveling above different finite-length gratings with a period of 2.5 mm.

A formal analysis of why heuristic functions work

Many optimization problems in computer science have been proven to be NP-hard, and it is unlikely that polynomial-time algorithms that solve these problems exist unless P = NP . Alternatively, they are solved using heuristics algorithms, which provide a sub-optimal solution that, hopefully, is arbitrarily close to the optimal. Such problems are found in a wide range of applications, including artificial intelligence, game theory, graph partitioning, database query optimization, etc. Consider a heuristic algorithm, A. Suppose that A could invoke one of two possible heuristic functions. The question of determining which heuristic function is superior, has typically demanded a yes/no answer—one which is often substantiated by empirical evidence. In this paper, by using Pattern Classification Techniques (PCT), we propose a formal, rigorous theoretical model that provides a stochastic answer to this problem. We prove that given a heuristic algorithm, A, that could utilize either of two heuristic functions H 1 or H 2 used to find the solution to a particular problem, if the accuracy of evaluating the cost of the optimal solution by using H 1 is greater than the accuracy of evaluating the cost using H 2 , then H 1 has a higher probability than H 2 of leading to the optimal solution. This unproven conjecture has been the basis for designing numerous algorithms such as the A* algorithm, and its variants. Apart from formally proving the result, we also address the corresponding database query optimization problem that has been open for at least two decades. To validate our proofs, we report empirical results on database query optimization techniques involving a few well-known histogram estimation methods.

In situ characterization of interface-microstructure dynamics in 3D-Directional Solidification of model transparent alloys

Microstructure plays a central role in determining properties of materials so that the fundamental understanding of the physics of microstructure selection is critical in the design of materials. Under terrestrial conditions fluid flow effects are dominant in bulk samples which preclude precise characterization of fundamental physics of microstructure selection. Experiments in thin samples, carried out to obtain diffusive growth, give microstructures that are neither 2D nor 3D. Rigorous theoretical models, using the phase-field method, have shown that the fundamental physics of pattern selection in 2D and 3D is significantly different. A benchmark experimental study is required in bulk samples under low gravity conditions. Also, the selection of microstructure occurs during the dynamical growth process so that in situ observations of spatio-temporal evolution of the interface shapes are required. Microgravity experiments on ISS are thus planned in a model transparent system by using a new Directional Solidification Insert (DSI), designed for use in the DECLIC facility of CNES and to be adapted to also fit ESA experiments. The critical aspects of hardware design, the key fundamental issues identified through 1g-experiments, the proposed experimental study on ISS, and the results of rigorous theoretical modeling are presented.

The role of adsorption in the catalytic electrode mechanism studied by means of square-wave voltammetry

A complex electrode mechanism coupled with adsorption of the redox couple and an irreversible homogeneous chemical reaction that regenerates the electroactive reactant is studied both theoretically and experimentally under conditions of square-wave voltammetry. The homogeneous regenerative redox reaction, i.e., the so-called catalytic reaction, takes place as a surface or volume process, depending on whether it includes the dissolved or adsorbed form of the electrode product, respectively. A rigorous theoretical model is presented considering simultaneously all relevant phenomena affecting the voltammetric response, such as mass transport, adsorption equilibria and kinetics of two different catalytic reactions, i.e., volume and surface catalytic reactions. The solutions for the surface concentration of the electroactive species are presented in the form of integral equations, thus they are general and valid for any chronoamperometric and voltammetric technique. The model enables systematic study of the role of adsorption in a complex catalytic electrode mechanism. The properties of the voltammetric response show remarkable discrepancies between the effect of the volume and surface catalytic reactions, thus enabling their recognition and separate characterization. From an analytical point of view it is demonstrated that the catalytic mechanism of moderate adsorption is superior in comparison with the pure volume and surface catalytic mechanisms. The theoretical predictions are confirmed by the voltammetric behaviour of the redox couple azobenzene/hydrazobenzene at the mercury electrode by using a mixture of water + acetonitrile as a solvent.

Necessity of investigating microstructure formation during directional solidification of transparent alloys in 3D

Abstract The properties of structural materials are to a large extent determined by the solid microstructure so that the understanding of the fundamental physics of microstructure formation is critical in the engineering of materials. Also, microstructure selection occurs during the dynamical growth process so that in situ observation of spatio-temporal evolution of the solid–liquid interface shape is necessary. Under terrestrial conditions convection effects dominate in bulk samples, which prevents precise characterization of microstructure selection. Diffusion-controlled experiments in thin samples give microstructures that are neither 2D nor 3D. Rigorous theoretical models using the phase-field method have shown that the fundamental physics of pattern selection in 2D and 3D is significantly different. A benchmark experimental study in bulk samples is thus required under low gravity conditions. In the frame of the joint work of DSIP and MISOL3D projects, respectively, selected by NASA and CNES, microgravity experiments in a model transparent system are planned on ISS using the directional solidification insert (DSI) in the DECLIC facility. The critical aspects of hardware design, the key fundamental issues identified through 1g-experiments, the proposed study on ISS, and the results of rigorous theoretical modeling are presented.

Mid-IR optical limiter based on type-II quantum wells

We show that strong optically induced intervalence band transitions in type-II InAs/GaSb/AlSb quantum wells lead to reverse saturable absorption, and propose to apply it to optical limiting in the mid-infrared spectral region. A salient feature of the proposed limiter is the flexibility of the design for different wavelengths and threshold powers. We develop a rigorous theoretical model of the proposed limiter, and use it to estimate the relationship between the key figures of merit: insertion loss, threshold, optical bandwidth and dynamic range. We investigate tradeoffs involving the dynamic range, optical bandwidth and thickness of the limiter, and show that one can attain a favorable combination of these.

Simultaneous Measurement of the Density and Viscosity of Compressed Liquid Toluene

A vibrating-wire densimeter described previously has been used to perform simultaneous measurements of the density and viscosity of toluene at temperatures from 222 to 348 K and pressures up to 80 MPa. The density measurements are essentially based on the hydrostatic weighing principle, using a vibrating-wire device operated in forced mode of oscillation, as a sensor of the apparent weight of a cylindrical sinker immersed in the test fluid. The resonance characteristics for the transverse oscillations of the wire, which is also immersed in the fluid, are described by a rigorous theoretical model, which includes both the buoyancy and the hydrodynamic effects, owing to the presence of the fluid, on the wire motion. It is thus possible, from the working equations, to determine simultaneously, both the density and the viscosity of the fluid from the analysis of the resonance curve of the wire oscillation, the density being related essentially to the position of the maximum and the viscosity to its width. New results of measurements of the density and viscosity of toluene in the compressed liquid region are presented, and compared with literature data. The density results extend over a temperature range 222 K≤T≤348 K, and pressures up to 80 MPa. The viscosity results cover a temperature range of 248 K≤T≤348 K and pressures up to 80 MPa. The uncertainty of the present density data is estimated to be within ±0.1% at temperatures 298 K≤T≤350 K, and ±0.15% at 222 K≤T≤273 K. The corresponding overall uncertainty of the viscosity measurements is estimated to be ±2% for temperatures 298 K≤T≤350 K, and ±3% for 248 K≤T≤273 K.

The linkage between magnesium binding and RNA folding

Understanding the linkage between Mg2+ binding and RNA folding requires a proper theoretical model describing the energetics of Mg2+ binding to the folded and unfolded states of RNA. Our current understanding of Mg2+ binding to these different RNA states derives from empirical thermodynamic models that depend on a number of unjustified assumptions. We present a rigorous theoretical model describing the linkage between RNA folding and magnesium ion binding. In this model, based on the non-linear Poisson-Boltzmann (NLPB) equation, the stabilization of RNA by Mg2+ arises from two distinct binding modes, diffuse binding and site binding. Diffusely bound Mg2+ are described as an ensemble of hydrated ions that are attracted to the negative charge of the RNA. Site-bound Mg2+ are partially desolvated ions that are attracted to electronegative pockets on the RNA surface. We explore two systems, yeast tRNAPhe and a 58-nucleotide rRNA fragment, with different Mg2+ binding properties. The NLPB equation accurately describes both the stoichiometric and energetic linkage between Mg2+ binding and RNA folding for both of these systems without requiring any fitted parameters in the calculation. Moreover, the NLPB model presents a well-defined physical description of how Mg2+ binding helps fold an RNA. For both of the molecules studied here, the relevant unfolded state is a disordered intermediate state (I) that contains stable helical secondary structure without any tertiary contacts. Diffusely bound Mg2+ interact with these secondary structure elements to stabilize the I state. The secondary structural elements of the I state fold into a compact, native tertiary structure (the N state). Diffuse binding plays a dominant role in stabilizing the N state for both RNAs studied. However, for the rRNA fragment, site-binding to a location with extraordinarily high electrostatic potential is also coupled to folding. Our results suggest that much experimental data measuring the linkage between Mg2+ binding and RNA folding must be reinterpreted.

Optical saturation in continuous-wave photothermal deflection spectroscopy: quantitative investigation of fundamental and harmonic components

A rigorous theoretical model has been developed that describes the effects of optical saturation on the deflection signals in cw photothermal experiments. In this model the spatial profile of the excitation beam has been taken into account. Numerical calculations have been performed to determine the saturation behavior of the cw photothermal deflection signals at both the fundamental and the second-harmonic frequencies for sine-wave modulation of the excitation beam. Saturation behavior for square-wave modulation has also been investigated.

Probing the surrounding of a cobalt(II) porphyrin and its superoxo complex by EPR techniques

Octaethylporphyrinato-cobalt(II), Co(II)OEP, was studied by electron paramagnetic resonance (EPR) and electron-nuclear double resonance (ENDOR) in frozen solutions of methanol, tetrahydrofuran and pyridine diluted into chloroform. Oxygenation led to the respective paramagnetic superoxo complexes Co(III)OEP · py · O 2 −⋅ The EPR spectra demonstrate strong differences in the axial ligation states ((base-on)/(base-off)) and ease of the oxygenation process. Additional ENDOR studies with partial orientation selection along the principalg tensor axes are performed for resolution of the1H,14/15N and59Co hyperfine coupling constants. This allows a comparison of the electron spin density distribution of the superoxo complex and its precursor. The data are interpreted in the framework of a more rigorous and detailed theoretical configuration interaction model than previously presented in the literature. The theoretical treatment shows that the structure of the superoxo complex is best described in a three-orbital model with contributions from the cobalt 3d, 4s, and oxygen π orbitals. The analysis reproduces the experimentalg and Co hyperfine data yielding the relative energies of the MO’s and the MO coefficients for the description of the spin density distribution in the Co(II) complex and its superoxo complex. To demonstrate the generality of the approach and possible applications, a comparison is made with the vitamin B12r system. Furthermore, it provides detailed insight into the electronic and geometric changes resulting from axial ligation and oxygenation of the Co(II)OEP complex; this information can be used for predictions of the catalytic activity.

Mg2+ binding to tRNA revisited: the nonlinear poisson-boltzmann model

Our current understanding of Mg2+ binding to RNA, in both thermodynamic and structural terms, is largely based on classical studies of transfer RNAs. Based on these studies, it is clear that magnesium ions are crucial for stabilizing the folded structure of tRNA. We present here a rigorous theoretical model based on the nonlinear Poisson-Boltzmann (NLPB) equation for understanding Mg2+ binding to yeast tRNAPhe. We use this model to interpret a variety of experimental Mg2+ binding data. In particular, we find that the NLPB equation provides a remarkably accurate description of both the overall stoichiometry and the free energy of Mg2+ binding to yeast tRNAPhe without any fitted parameters. In addition, the model accurately describes the interaction of Mg2+ with localized regions of the RNA as determined by the p Ka shift of differently bound fluorophores. In each case, we find that the model also reproduces the univalent salt-dependence and the anticooperativity of Mg2+ binding. Our results lead us to a thermodynamic description of Mg2+ binding to yeast tRNAPhe based on the NLPB equation. In this model, Mg2+ binding is simply explained by an ensemble of ions distributed according to a Boltzmann weighted average of the mean electrostatic potential around the RNA. It appears that the entire ensemble of electrostatically bound ions superficially mimics a few strongly coordinated ions. In this regard, we find that Mg2+ stabilizes the tertiary structure of yeast tRNAPhe in part by accumulating in regions of high negative electrostatic potential. These regions of Mg2+ localization correspond to bound ions that are observed in the X-ray crystallographic structures of yeast tRNAPhe. Based on our results and the available thermodynamic data, there is no evidence that specifically coordinated Mg ions have a significant role in stabilizing the native tertiary structure of yeast tRNAPhe in solution.

Formation des bulles dans les fluide newtoniens et non newtoniens

The present study aims at providing insights into the understanding of the formation of bubbles at a submerged orifice under constant flow conditions, in both Newtonian and non-Newtonian fluids. A rigorous theoretical model was developed for describing the non-spherical bubble formation as well as the detachment at the orifice. The results predicted by this model compare satisfactorily with the experimental investigation. However, a deviation was observed in elastic fluids with the increase of gas flow rates when the memory effects become important.

Optical characterization of a complex grating profile

The grating studied here, produced by interferographic exposure of photoresist, comprises two gratings, one with twice the period of the other, aligned so that their Bragg vectors are separated by an angle of 0.02°. Thus, as one moves along the grooves, these two gratings locally vary their relative phase. Coating this grating with metal allows the optical characterization of this surface by the excitation of surface plasmon polaritons. This paper starts by demonstrating the inability of a profilometer to profile accurately the surface of this bi-grating because of the limitations imposed by the finite width of the stylus on the scale of the grating grooves. Angle-dependent reflectivity data are then used to characterize the metal-coated surface. The size and shape of the surface plasmon resonances in these data, once matched to a rigorous theoretical model, are shown to provide a quantification of the surface profile. This accords with both the profile expected from the limited profilometer study, and more significantly with the surface function predicted using a simple model of the photoresist's response to exposure.

The effect of interface resistances on thermal wave propagation in multi-layered samples

In this paper a rigorous three-dimensional theoretical model describing the temperature distribution in multi-layered samples, heated by an intensity-modulated Gaussian laser beam, is presented. The thermal interface resistances and the thermal conductivity anisotropy of one of the layers are taken into consideration. The three-dimensional thermal diffusion model is used to investigate the effect of thermal interface resistances on thermal conduction in three-layered samples, which is monitored in terms of the dependences of the amplitude and phase of the surface temperature rise of the sample on the modulation frequency of the excitation beam. The theoretical results can be used as a means of quantitative interpretation for the determination of interfacial thermal resistances in layered materials with modulated photothermal techniques. A direct comparison between the one- and three-dimensional theoretical models for thermal conduction in layered materials is also presented.

Output signal and noise characteristics in RF pumped double SQUIDS

On the base of a rigorous theoretical model the output characteristics of a RF double SQUID for use as an instrument for delicate measurements are computed, and the two RF pump modes (external and autodyne) are optimized from the output signal level point of view. Then, a two-dimensional thermal activation model is applied for the analysis of the intrinsic noise influence on the output performances of such a device. A theoretical estimation for the flux noise spectral densities at low frequencies is given and an optimization from the signal-to-noise ratio and double SQUID flux coupling points of view is also made. Showing the superiority of this novel RF pumped SQUID configuration over the traditional one, both these theoretical approaches gave results that are in a very good agreement with the existed experimental data.

Characterization of a grating-coupled liquid crystal cell using a rigorous theoretical model

We use a rigorous differential formalism to model the optical response of a multilayer structure having both a surface-relief grating and containing uniaxial materials. The uniaxial material is, in this case, a layer of liquid crystal that has its uniaxial axis defined by its director. By fitting experimental angle dependent reflectivity data to a multilayer grating model we are able to determine the spatial profile of the liquid crystal director, and show how accurately the optical response of such a system may be modelled.