Assuming linear theory, the phenomenon of scattering of waves by a circular arc shaped barrier with nonuniform porosity is studied. The water region is considered to be of infinite or finite depth. Based on a judicious application of Green’s integral theorem, the corresponding boundary value problem is reduced to a hypersingular integral equation of second kind. The boundary element method and the collocation method are adopted to solve the hypersingular integral equation, and we ensure a good matching of the solutions obtained by the two methods. The reflection coefficient and energy dissipation are evaluated by using the solution of the integral equation which is then studied graphically. Different choices of distributions of pores on the barrier are considered, and we observe that the nonuniform porosity of the barrier has significant effect on the reflected wave and the energy dissipation.

The results of a combined chemico-osmotic/diffusion experiment conducted on a geosynthetic clay liner (GCL) containing Na-bentonite illustrate the destructive role of diffusion on the ability of the GCL to act as a semipermeable membrane. The experiment is conducted by maintaining a concentration difference of 5 mM CaCl2 across the GCL specimen while preventing the flow of solution through the specimen. A time-dependent membrane efficiency is derived from measured pressure differences induced across the specimen in response to the applied concentration difference. The diffusive mass fluxes of the solutes (Cl− and Ca2+) through the specimen are also measured simultaneously. An initial increase in induced pressure difference across the specimen to a peak value of 19.3 kPa is observed, followed by a gradual decrease to zero. The decrease in induced pressure difference is consistent with compression of diffuse double layers between clay particles and particle clusters due to diffusion of Ca2+, resulting in a concomitant increase in pore sizes and decrease in the observed membrane behavior. The time required for effective destruction of the initially observed semipermeable membrane behavior correlates well with the time required to achieve steady-state Ca2+ diffusion. The results have important implications for the ability of clays to sustain membrane behavior.

The ability of food products to store and dissipate electromagnetic energy is determined by the material's dielectric properties. In relation to this phenomenon, a non-destructive technique is presented for food evaluation based on the shift in resonant frequency and reflection coefficient magnitude value of the proposed slot-loaded microstrip line-fed antenna-based sensor caused by the change in dielectric properties of the food material. In this work, a miniaturized antenna sensor of 10 × 10 mm2 size comprised of a dielectric substrate FR-4 with permittivity (εr) = 4.4 having ground plane at the bottom and a radiating element at the top is designed to operate at 13.3 GHz. Three samples of spices, i.e. red chilli powder, black pepper powder, and turmeric powder, are considered for quality monitoring whose relationship in terms of reflection coefficient, resonant frequency, and dielectric permittivity at 13.17, 12.61, and 13.09 GHz respectively is analyzed. Further, second-order polynomial model is derived to predict dielectric permittivity of the material under test with high accuracy. The experimental procedure of this proposed sensor is based upon the interaction of the sample food materials with the electromagnetic field owing to shift in resonant frequency as a function of dielectric permittivity of the samples. The proposed antenna sensor has a Q-factor of 409, showing significantly high sensitivity of 280 MHz with 98% accuracy and standard deviation less than the difference between unadulterated and adulterated values, giving resolution high enough to distinguish adulteration with an acceptable statistical accuracy.

In this study, a novel microstrip antenna sensor with defected ground structure is investigated to detect the presence of other substances in liquid food samples. The proposed antenna sensor is rake-shaped which has been designed using time domain solver in three-dimensional simulation software Computer Simulation Technology Microwave Studio. The proposed antenna sensor has been fabricated using an FR4 material, having overall dimensions of 30 × 27 mm2 with dielectric constant 4.4, substrate thickness 1.57 mm, and loss tangent 0.0025. Furthermore, the Q-factor of the proposed antenna sensor is 485 showing a maximum sensitivity of 700 MHz and having accuracy 98%. In the present work, water and juice are considered as liquid samples in which the presence of foreign substances is detected in terms of reflection coefficient and shift in resonant frequency with the help of the suggested microstrip antenna sensor. Through experimentation, it has been observed that with the increase in the percentage of adulterant in the considered samples, the dielectric property of solution changes which results in shift of reflection coefficient and resonant frequency, thus making an allowance for the proposed antenna sensor a valid tool to detect adulteration in liquid samples.

An inscribed hexagonal fractal slotted patch antenna with some additional geometry and slots is proposed for the optimization in this paper. This research work is concerned with the optimization of this slotted fractal antenna with the help of the curve-fitting method in conjunction with the modified version of Lightning Attachment Procedure Optimization (MLAPO) technique. The data required for the curve-fitting technique and for the optimization technique have been obtained by varying some of the parameters of the proposed antenna. Different equations are developed to know the relations between these parameters of the proposed antenna. The MLAPO technique is applied thereafter to calculate the different optimized geometrical parameters to optimize the bandwidth for the proposed antenna. The optimized geometrical parameters are verified with the help of a parametric variation to justify the reliable optimization. The bandwidth obtained by the MLAPO technique has been found to be better than that obtained by PSO and normal LAPO algorithm. The prototype of the optimized antenna is fabricated and the experimental results are found to be compatible with the results obtained by simulation. The proposed optimized antenna may be utilized in various applications in C and X bands.

Explicit solutions are rarely available for water wave scattering problems. An analytical procedure is presented here to solve the boundary value problem associated with wave scattering by a complete vertical porous barrier with two gaps in it. The original problem is decomposed into four problems involving vertical solid barriers. The decomposed problems are solved analytically by using a weakly singular integral equation. Explicit expressions are obtained for the scattering amplitudes and numerical results are presented. The results obtained can be used as a benchmark for other wave scattering problems involving complex geometrical structures.

We study the reflection of membrane-coupled gravity waves in deep water against a vertical barrier with a gap. A floating membrane is attached on both sides of the barrier. The associated mixed boundary value problem, which is not particularly well posed, is analysed. We utilize an orthogonal mode-coupling relation to reduce the problem to solving a set of dual integral equations with trigonometric kernel. We solve these by using a weakly singular integral equation. The reflection coefficient is determined explicitly, while having freedom to clamp the membrane with a spring of a certain stiffness on only one side of the vertical barrier. The physical problem is of capillary–gravity wave scattering by a vertical barrier with a gap, when the membrane density is neglected. In this case, the reflection coefficient is known up to an undetermined edge slope on either side of the barrier. The scattering quantity is computed and presented graphically against a wave parameter for different values of nondimensional parameters pertaining to the structures involved in the problem.

Matching boundary conditions (MBC’s) are proposed to treat scalar waves in the body-centered-cubic lattices. By matching the dispersion relation, we construct MBC’s for normal incidence and incidence with an angle α. Multiplication of MBC operators then leads to multi-directional absorbing boundary conditions. The effectiveness are illustrated by the reflection coefficient analysis and wave packet tests. In particular, the designed M1M1 treats the scalar waves in a satisfactory manner.

Scattering of membrane coupled gravity waves in deep water by partial vertical barriers is investigated by the recently developed expansion formulae for wave structure interaction problems. The horizontal thin membrane is considered to be under uniform tension and is covering the free surface. The analysis is based on the linearized theory of water waves, and by combining the kinematic and dynamic conditions at the membrane covered surface, one may derive a not so well-posed mixed boundary value problem for Laplace’s equation with third-order boundary condition. The flexible membrane is attached by a spring to the surface piercing barrier, giving suitable edge conditions for the unique solution. The boundary value problem has been converted into dual integral equations with kernels composed of trigonometric functions, which are then solved analytically. The important physical quantities such as reflection and transmission coefficients for both cases of submerged and surface piercing barriers are obtained analytically in terms of modified Bessel functions. It is found that complete reflection or transmission is possible at certain resonant frequencies for the incident membrane coupled waves. Numerical results are plotted and discussed for different values of the nondimensional membrane tension parameter.

A general theorem on the GBDT version of the Bäcklund-Darboux transformation for systemsdepending rationally on the spectral parameter is treated and its applications tononlinear equations are given. Explicit solutions of direct and inverse problems forDirac-type systems, including systems with singularities, and for the system auxiliary tothe N-wave equation are reviewed. New results on explicit construction ofthe wave functions for radial Dirac equation are obtained.