Some Theoretical and Experimental Extensions Based on the Properties of the Intrinsic Transfer Matrix

The work approaches new theoretical and experimental studies in the elastic characterization of materials, based on the properties of the intrinsic transfer matrix. The term ‘intrinsic transfer matrix’ was firstly introduced by us in order to characterize the system in standing wave case, when the stationary wave is confined inside the sample. An important property of the intrinsic transfer matrix is that at resonance, and in absence of attenuation, the eigenvalues are real. This property underlies a numerical method which permits to find the phase velocity for the longitudinal wave in a sample. This modal approach is a numerical method which takes into account the eigenvalues, which are analytically estimated for simple elastic systems. Such elastic systems are characterized by a simple distribution of eigenmodes, which may be easily highlighted by experiment. The paper generalizes the intrinsic transfer matrix method by including the attenuation and a study of the influence of inhomogeneity. The condition for real eigenvalues in that case shows that the frequencies of eigenmodes are not affected by attenuation. For the influence of inhomogeneity, we consider a case when the sound speed is varying along the layer’s length in the medium of interest, with an accompanying dispersion. The paper also studies the accuracy of the method in estimating the wave velocity and determines an optimal experimental setup in order to reduce the influence of frequency errors.

Solvability of Some Nonlocal Fractional Boundary Value Problems at Resonance in Rn

In this paper, the solvability of a system of nonlinear Caputo fractional differential equations at resonance is considered. The interesting point is that the state variable x∈Rn and the effect of the coefficient matrices matrices B and C of boundary value conditions on the solvability of the problem are systematically discussed. By using Mawhin coincidence degree theory, some sufficient conditions for the solvability of the problem are obtained.

ABOUT THE ACCELERATION RATE OF RELATIVISTIC BEAMS BY A SURFACE WAVE IN A DIELECTRIC LASER ACCELERATOR

An analysis of the dependence of the acceleration rate of charged particles by a surface wave arising when a la-ser pulse/(plane wave) is incident on the interface between two dielectric media on the phase velocity of the excited wave is carried out. It is shown that at resonance acceleration this dependence has a maximum, for ultra-relativistic particles the acceleration rate tends to zero. The dependences of the acceleration rate on the phase velocity of the excited wave for various refractive indices (dielectric permittivities) of optically transparent medias are investigated analytically and numerically.

Mawhin’s Continuation Technique for a Nonlinear BVP of Variable Order at Resonance via Piecewise Constant Functions

In this paper, we establish the existence of solutions to a nonlinear boundary value problem (BVP) of variable order at resonance. The main theorem in this study is proved with the help of generalized intervals and piecewise constant functions, in which we convert the mentioned Caputo BVP of fractional variable order to an equivalent standard Caputo BVP at resonance of constant order. In fact, to use the Mawhin’s continuation technique, we have to transform the variable order BVP into a constant order BVP. We prove the existence of solutions based on the existing notions in the coincidence degree theory and Mawhin’s continuation theorem (MCTH). Finally, an example is provided according to the given variable order BVP to show the correctness of results.

High-Q two-groove resonator for all-dielectric Bloch surface wave platform

We propose a simple integrated resonant structure for the Bloch surface wave platform, which consists of two subwavelength grooves patterned on the surface of a one-dimensional dielectric photonic crystal. We demonstrate that the investigated structure can operate in a parasitic-scattering-free regime and, in this case, provide unity transmittance and zero reflectance at resonance conditions associated with the excitation of a leaky mode of the structure localized at the central ridge formed by the grooves. The proposed structure may find application in integrated photonic devices for optical filtering and analog optical computing.

A Fundamental Study to Observe Correlation at Molecular Level between Bio-Samples of Patients and Indicated Homoeopathic Medicines

Background: ‘Like cures like’ is the principle that is followed in homoeopathy. Substances which cause disorder in healthy individuals are used as medicines to treat similar patterns of disorder in sick persons. This article aims to find out whether any similarity picture exists at molecular level also that can make a selection of medicines based on scientifically measurable parameters. Method: It consisted of getting frequency domain signatures for the dielectric functions of (i) bio-fluids (blood serums) of six arthritis patients and (ii) medicines selected for them on the basis of macroscopic similarity. Then, they were compared to find existence/absence of similarity between them. Results: Medicines administered to the six patients were Rhus tox 200cH, Thuja 30cH, Medorrhinum 200cH. The dielectric loss at resonance for the bio-fluids of the patients and the medicines are given in the body of the article. Conclusion: It was observed that the patients who had beneficial results with their medicines have a similarity (resonance frequency matching) in spectral signatures of the two groups of substances i.e. bio-fluids (blood serum) of patients and the indicated remedies. This similarity was not evident in the cases where medicines failed to benefit the patients. These results are explorative and enthusiastic, but as the research is limited only to patients with arthritis, generalization could not be drawn. Further work with more rigor is required to establish the facts and apply generalizations to other disease condition. In future, this might be a new tool to integrate the fundamental research with clinical applications in homeopathy.