Light Scattering by a Subwavelength Plasmonic Array: Anisotropic Model

We calculate the light transmission by a subwavelength plasmonic array using the boundary element method for parallel cylinders with different cross-sections: circular or elliptic with axis ratio 4:1. We demonstrate that plasmonic resonance is sharper for the case of horizontal ellipses. This structure is susceptible to refractive index variations in the media since the high derivatives of reflection and transmission coefficients are near the angle of total internal reflection. To obtain an approximate analytical expression, we used the model of a metallic layer. We explore the “sandwich” structure with an anisotropic film between two dielectrics and demonstrate its quantitative agreement with numerical results.

Study on energy and information-entropic measures of Hulthén potential in D dimension by an intuitive approximation to centrifugal term

Energy spectrum as well as various information theoretic measures are considered for Hulthén potential in D dimension. For a given ℓ≠0 state, analytic expressions are derived, following a simple intuitive approximation for accurate representation of centrifugal term, within the conventional Nikiforov-Uvarov method. This is derived from a linear combination of two widely used Greene-Aldrich and Pekeris-type approximations. Energy, wave function, normalization constant, expectation value in r and p space, Heisenberg uncertainty relation, entropic moment of order α¯, Shannon entropy, Rényi entropy, disequilibrium, majorization as well as four selected complexity measures like LMC (López-Ruiz, Mancini, Calbert), shape Rényi complexity, Generalized Rényi complexity and Rényi complexity ratio are offered for different screening parameters (δ). The effective potential is described quite satisfactorily throughout the whole domain. Obtained results are compared with theoretical energies available in literature, which shows excellent agreement. Performance of six different approximations to centrifugal term is critically discussed. An approximate analytical expression for critical screening for a specific state in arbitrary dimension is offered. Additionally, some inter-dimensional degeneracy occurring in two states, at different dimension for a particular δ is also uncovered. PACS: 02.60.-x, 03.65.Ca, 03.65.Ge, 03.65.-w Keywords: Hulthén potential, Rényi complexity ratio, Statistical complexity, Majorization, Pekeris approximation, Greene-Aldrich approximation.

Scalar Casimir effect for a conducting cylinder in a Lorentz-violating background

Following a field-theoretical approach, we study the scalar Casimir effect upon a perfectly conducting cylindrical shell in the presence of spontaneous Lorentz symmetry breaking. The scalar field is modeled by a Lorentz-breaking extension of the theory for a real scalar quantum field in the bulk regions. The corresponding Green’s functions satisfying Dirichlet boundary conditions on the cylindrical shell are derived explicitly. We express the Casimir pressure (i.e. the vacuum expectation value of the normal–normal component of the stress–energy tensor) as a suitable second-order differential operator acting on the corresponding Green’s functions at coincident arguments. The divergences are regulated by making use of zeta function techniques, and our results are successfully compared with the Lorentz invariant case. Numerical calculations are carried out for the Casimir pressure as a function of the Lorentz-violating coefficient, and an approximate analytical expression for the force is presented as well. It turns out that the Casimir pressure strongly depends on the Lorentz-violating coefficient and it tends to diminish the force.

The Effect of Radiotherapy on Diffuse Low-Grade Gliomas Evolution: Confronting Theory with Clinical Data

Diffuse low-grade gliomas are slowly growing tumors that always recur after treatment. In this paper, we revisit the modeling of the evolution of the tumor radius before and after the radiotherapy process and propose a novel model that is simple yet biologically motivated and that remedies some shortcomings of previously proposed ones. We confront this with clinical data consisting of time series of tumor radii from 43 patient records by using a stochastic optimization technique and obtain very good fits in all cases. Since our model describes the evolution of a tumor from the very first glioma cell, it gives access to the possible age of the tumor. Using the technique of profile likelihood to extract all of the information from the data, we build confidence intervals for the tumor birth age and confirm the fact that low-grade gliomas seem to appear in the late teenage years. Moreover, an approximate analytical expression of the temporal evolution of the tumor radius allows us to explain the correlations observed in the data.

A Novel Version of HPM Coupled with the PSEM Method for Solving the Blasius Problem

This work studies the nonlinear differential equation that models the Blasius problem (BP) which is of great importance in fluid dynamics. The aim is to obtain an approximate analytical expression that adequately describes the phenomenon considered. To find such approximation, we propose a new method denominated powered homotopy perturbation (PHPM). Unlike HPM algorithm, the successive integration process generated by PHPM will consider zero the constants of integration in each approximation, except the last one. In the same way, PHPM will propose an adequate initial trial function provided of some unknown parameters in such a way that it will not evaluate the initial conditions in the iterations of the process; therefore, this set of parameters will be employed with the purpose of adjusting in the best accurate way the proposed approximation at the final part of the process. As a matter of fact, we will note from this analysis that the proposed solution is compact and easy to evaluate and involves a sum of five exponential functions plus a linear part of two terms, which is ideal for practical applications. With the purpose to get a better approximation, we find useful to combine PHPM with the power series extender method (PSEM) which implies to add to the PHPM solution one rational function with parameters to adjust. From this proposal, we find an approximate solution competitive with others from the literature.

Approximate Calculation and Feature Analysis of Electric Field in Space by Thunderclouds

The calculation of electric field in space excited by thunderclouds is an important basis for lightning warning and protection. In numerical calculation of the electromagnetic field, it is often necessary to perform multiple loop nesting calculations on several triple integrals, which consume a lot of computing resources. In order to shorten the calculation time and improve the calculation efficiency, the electric field excited by the charged thunderclouds in space is theoretically derived with the analytical method by the thundercloud cylindrical charge pile model and based on the electrostatic field theory. The complex integrand function is approximated, so that the analytic expression of electric field in space is obtained in this paper. Through simulation and comparison, it is found that the approximate solution and the exact solution are similar in size, the change trend is the same, and the approximate analytical expression can be used for the approximate calculation of the electric field in a short range. Under certain conditions, the approximate solution can be converted into an accurate solution, which can be used for the accurate calculation of the electric field. Approximate calculation not only simplifies theoretical derivation but also improves calculation efficiency. The calculation time has been shortened from tens of hours to less than one second by using different calculation methods, which is a difference of 7 orders of magnitude. With approximate analytical expression, the electric field excited by charge pile with typical structures in thunderclouds in space is calculated and the characteristics of that are analyzed in this paper. For lightning protection of mobile targets, approximate calculation is of great significance in shortening the lightning warning time and enhancing the protection effect.

Slow flow solutions and stability analysis of single machine to infinite bus power systems

Nonlinearity is a major constraint in analysing and controlling power systems. The behaviour of the nonlinear systems will vary drastically with changing operating conditions. Hence a detailed study of the response of the power system with nonlinearities is necessary especially at frequencies closer to natural resonant frequencies of machines where the system may jump into the chaos. This paper attempt such a study of a single machine to infinite bus power system by modelling it as a Duffing equation with softening spring. Using the method of multiple scales, an approximate analytical expression which describes the variation of load angle is derived. The phase portraits generated from the slow flow equations, closer to the jump, display two stable equilibria (centers) and an unstable fixed point (saddle). From the analysis, it is observed that even for a combination of parameters for which the system exhibits jump resonance, the system will remain stable if the variation of load angle is within a bounded region.

Analysis of Biodegradation and Microbial Growth in Groundwater System Using New the Homotopy Perturbation Method

In this paper, we drive the concentration of microbial growth in the groundwater system. This model is based on the system of non-linear differential equations. The system of equations is solved by using the new homotopy perturbation method. We followed toluene degradation and bacterial growth by measuring toluene and oxygen concentrations and by direct cell counts. And the total amount of toluene degraded by Pseudomonal putida F1 in the sediment columns increased with rising concentration of the source and flow rate. In contrast, the efficiency of toluene removal slowly decreases. The approximate analytical expression of this model, the concentration of toluene and bacteria also consideration of a metabolite concentration, the microbial growth of attached and suspended bacteria, depending on the simultaneous presence of toluene. Finally, oxygen and dual Monod kinetics are discussed. The analytical solutions are also compared with simulation results and satisfactory the agreement is noted.

Mathematical Modeling of Bio Hydrogen Production in Microbial Electrolysis Cell Reactor

Mathematical modeling of biohydrogen production in microbial electrolysis cell reactor is discussed. This study explains the mathematical model for the production of hydrogen from a wastewater batch reactor, and it contains a system of non-linear equations. The non-linear differential equation of this model is solved by the Homotopy perturbation method. The approximate analytical expression of this model, concentration of substrate, anodophilic microorganisms, acetoclastic microorganism, hydrogenotrophic microorganisms, and Oxidized mediator are obtained. The effect of various values of the parameters on the reactions is discussed. The analytical solutions are also compared with simulation results and satisfactory the agreement is noted.

Approximate analytical analysis of longitudinal natural frequencies of a cracked beam

PurposeIn this paper, an approximate analytical approach is developed for the determination of natural longitudinal frequencies of a cantilever-cracked beam based on the Lagrange inversion theorem.Design/methodology/approachThe crack is modeled by an equivalent axial spring with stiffness according to Castigliano's theorem. Thus, an implicit frequency equation corresponding to cantilever-cracked bar is obtained. The resulting equation is solved using the Lagrange inversion theorem.Findingseffect of different crack depths and crack positions on natural frequencies of the cracked beam is analyzed. It is shown that an increase in the crack depth ratio produces a decrease in the fundamental longitudinal natural frequency of a cracked bar. Furthermore, approximate analytical results are compared with those obtained numerically as well as from experimental tests.Originality/valueA new approximate analytical expression of a fundamental longitudinal frequency, as a function of crack depth and crack location, is obtained.