Airy beam laser

A method to design lasers that emit an arbitrary beam profile is studied. In these lasers, output-coupling is performed by a diffraction grating that imposes a phase and amplitude distribution onto the diffracted light. A solid-state laser emitting beams with a two-dimensional Airy intensity profile is demonstrated both theoretically and experimentally. In this case, the diffraction grating adds a transverse cubic phase to the diffracted light. An Airy beam is obtained by performing optical Fourier transform of the out-coupled light. The laser beam profile and power characteristics are shown to agree with theory.     

Chitosan Nanoparticles-Insight into Properties,Functionalization and Applications in Drug Delivery and Theranostics

Nanotechnology-based development of drug delivery systems is an attractive area of research in formulation driven R&D laboratories that makes administration of new and complex drugs feasible. It plays a significant role in the design of novel dosage forms by attributing target specific drug delivery, controlled drug release, improved, patient friendly drug regimen and lower side effects. Polysaccharides, especially chitosan, occupy an important place and are widely used in nano drug delivery systems owing to their biocompatibility and biodegradability. This review focuses on chitosan nanoparticles and envisages to provide an insight into the chemistry, properties, drug release mechanisms, preparation techniques and the vast evolving landscape of diverse applications across disease categories leading to development of better therapeutics and superior clinical outcomes. It summarizes recent advancement in the development and utility of functionalized chitosan in anticancer therapeutics, cancer immunotherapy, theranostics and multistage delivery systems.     

Maximal Operators in the Spherical Mean Setting

In this paper, we prove an existence result for \(\mathcal {L}^{\infty }\)-solutions for a class of semilinear delay evolution inclusions with measures and subjected to nonlocal initial conditions of the form

$$\begin{aligned} \left\{ \begin{array}{ll} \displaystyle \mathrm{d}u(t)= \{Au(t)+f(t)\}\mathrm{d}t+\mathrm{d}h(t),&{}\quad t\in \mathbb {R}_+,\\ \displaystyle f(t)\in F(t,u_t),&{}\quad t\in \mathbb {R}_+,\\ \displaystyle u(t)=g(u)(t),&{}\quad t\in [\,-\tau ,0\,]. \end{array} \right. \end{aligned}$$

Here \(\tau \ge 0\), X is a Banach space, \(A:D(A)\subseteq X \rightarrow X \) is the infinitesimal generator of a \(C_0\)-semigroup, \(F:\mathbb {R}_+\times \mathcal {R}([\,-\tau ,0\,];X)\rightsquigarrow X\) is a u.s.c. multifunction with nonempty, convex and weakly compact values, \(h\in BV_{\mathrm{loc}}(\mathbb {R}_+;X)\) and the function \(g:\mathcal {R}_{b}(\mathbb {R}_+;X)\rightarrow \mathcal {R}([\,-\tau ,0\,];X)\) is nonexpansive.

     

Variational Solutions for Resonances by a Finite-Difference Grid Method

We demonstrate that the finite difference grid method (FDM) can be simply modified to satisfy the variational principle and enable calculations of both real and complex poles of the scattering matrix. These complex poles are known as resonances and provide the energies and inverse lifetimes of the system under study (e.g., molecules) in metastable states. This approach allows incorporating finite grid methods in the study of resonance phenomena in chemistry. Possible applications include the calculation of electronic autoionization resonances which occur when ionization takes place as the bond lengths of the molecule are varied. Alternatively, the method can be applied to calculate nuclear predissociation resonances which are associated with activated complexes with finite lifetimes.     

Peak intensity measurement of relativistic lasers via nonlinear Thomson scattering

The measurement of peak laser intensities exceeding 10(20) W/cm(2) is in general a very challenging task. We suggest a simple method to accurately measure such high intensities up to about 10(23) W/cm(2), by colliding a beam of ultrarelativistic electrons with the laser pulse. The method exploits the high directionality of the radiation emitted by ultrarelativistic electrons via nonlinear Thomson scattering. Initial electron energies well within the reach of laser wake-field accelerators are required, allowing in principle for an all-optical setup. Accuracies of the order of 10% are theoretically envisaged.     

Sol–gel synthesis and luminescent properties of SiO2/Zn2SiO4 and SiO2/Zn2SiO4:V composite materials

Undoped and vanadium-doped Zn₂SiO₄ particles embedded in silica host matrix were prepared by a simple solid-phase reaction after the incorporation of ZnO and ZnO:V nanoparticles, respectively, in silica monolith using the sol–gel method with supercritical drying of ethyl alcohol in two steps. After supercritical drying and annealing in the temperature range between 1423 and 1473 K in an air atmosphere, the photoluminescence (PL) measurements show a band centered at about 760 nm in the case of non-doped Zn₂SiO₄ which is attributed to energy transfer from Zn₂SiO₄ particles to NBOHs interface defects. In the case of vanadium doped Zn₂SiO₄, the PL reveals a band centered at about 540 nm attributed to the vanadium in the interfaces between Zn₂SiO₄ particles and SiO₂ host matrix. Photoluminescence excitation (PLE) measurements show different origins of the emission bands. The PLE band (～240–350 nm) may be understood as an energy transfer process from O^2? to V⁵⁺ which occurs intrinsically in the vanadyl group.     

Existence of Gibbs measures for countable Markov shifts

We prove that a potential with summable variations and finite pressure on a topologically mixing countable Markov shift has a Gibbs measure iff the transition matrix satisfies the big images and preimages property. This strengthens a result of D. Mauldin and M. Urbanski (2001) who showed that this condition is sufficient.

     

Effective properties of fiber and platelet systems and related phase arrangements in n-phase heterogenous media

For the structures which are neither aggregates nor inclusion-reinforced matrices, relevant property estimates are missing. We address composites with several, all or none co-continuous phases. Property estimates from various fibre systems and platelet systems that are likely to well approach the effective properties of such microstructures are examined. We provide arguments in favour of the relevancy of some of the investigated systems to represent phase co-continuity (or co-discontinuity), the reported results being supported by theoretical, topological and experimental considerations. The discussion is held in the linear elasticity framework with open extensions to other properties and behaviours.     

Synthesis,structural and complex impedance spectroscopy studies of Ni0.4Co0.4Mg0.2Fe2O4 spinel ferrite

Spinel ferrite having composition Ni_0.4Co_0.4Mg_0.2Fe₂O₄ was prepared by sol-gel method. X-ray diffraction result indicates that the ferrite sample has a cubic spinel type structure. FT-IR showed two absorption bands (ν₁ and ν₂) that are attributed to the stretching vibration of tetrahedral and octahedral sites. Complex impedance properties have been investigated in 200–420 K temperature range with varying frequency between 40 and 10⁷ Hz. Frequency and temperature dependency of imaginary part of permittivity (?″) and dielectric loss (tanδ) has been discussed in terms of hopping of charge carriers between Fe²⁺ and Fe³⁺ ions. Activation energy has been estimated from both temperature dependency of dc conductivity and relaxation time data, which indicates that the relaxation process and conductivity have the same origin. Nyquist plots of impedance show semicircle arcs for sample and an electrical equivalent circuit has been proposed to explain the impedance results.