Strong solutions and trajectory attractors to the thin-film equation with absorption

We prove local and global in time existence of non-negative weak solutions to the thin-film equation with absorption and obtain sufficient conditions for extra regularity of these solutions. Moreover, for the class of global strong solutions, we show existence of a trajectory attractor.     

Trapping photon-dressed Dirac electrons in a quantum dot studied by coherent two dimensional photon echo spectroscopy

We study the localization of dressed Dirac electrons in a cylindrical quantum dot (QD) formed on monolayer and bilayer graphene by spatially different potential profiles. Short lived excitonic states which are too broad to be resolved in linear spectroscopy are revealed by cross peaks in the photon-echo nonlinear technique. Signatures of the dynamic gap in the two-dimensional spectra are discussed. The effect of the Coulomb induced exciton-exciton scattering and the formation of biexciton molecules are demonstrated.     

Comparative solubilisation of potassium carbonate, sodium bicarbonate and sodium carbonate in hot dimethylformamide: application of cylindrical particle surface-controlled dissolution theory

A surface-controlled dissolution of cylindrical solid particles model is applied to potassium carbonate, sodium bicarbonate and sodium carbonate in dimethylformamide at elevated temperatures. Previously published data for the dissolution of potassium carbonate is interpreted assuming a cylindrical rather than a spherical shape of the particles, the former representing a closer approximation to the true shape of the particles as revealed by scanning electron microscopy. The dissolution kinetics of sodium carbonate and sodium bicarbonate in dimethylformamide at 100 degrees C were investigated via monitoring of the deprotonation of 2-cyanophenol with dissolved solid to form the 2-cyanophenolate anion that was detected with UV-visible spectroscopy. From fitting of experimental results to theory, the dissolution rate constant, k, for the dissolutions of potassium carbonate, sodium bicarbonate and sodium carbonate in dimethylformamide at 100 degrees C were found to have the values of (1.0 +/- 0.1) x 10(-7) mol cm(-2) s(-1), (5.5 +/- 0.3) x 10(-9) mol cm(-2) s(-1) and (9.7 +/- 0.8) x 10(-9) mol cm(-2) s(-1), respectively.     

Anomalous photon-assisted tunneling in graphene

We investigated the transmission of Dirac electrons through a potential barrier in the presence of circularly polarized light. An anomalous photon-assisted enhanced transmission is predicted and explained. It is demonstrated that the perfect transmission for nearly head-on collision in infinite graphene is suppressed in gapped dressed states of electrons, which is further accompanied by a shift of peaks as a function of the incident angle away from head-on collision. In addition, the perfect transmission is partially suppressed by a photon-induced gap in illuminated graphene. After the effect of rough edges of the potential barrier or impurity scattering is included, the perfect transmission with no potential barrier becomes completely suppressed and the energy range for the photon-assisted transmission is reduced at the same time.     

Passive nonlinear reshaping towards parabolic pulses in the steady-state regime in optical fibers

The passive nonlinear reshaping in normally dispersive optical fibers in the steady-state regime is studied numerically. It is found that normal dispersion and self-phase modulation are able to provide pulse reshaping towards a parabolic pulse profile at the distances exceeding the optical wave breaking length. However, as compared to the similariton formation in active fibers the resulted pulse shape in passive fibers is strongly depended on the initial pulse parameters and nonlinear and dispersive fiber properties as well. The influence of initial pulse shape, initial chirp, third-order dispersion and loss on the parabolic pulse formation is studied consistently, and estimation of practical conditions which are needed for parabolic pulses formation in a passive fiber is provided.     

Charge transport in polyaniline doped with 3-nitro-1,2,4-triazol-5(4H)-one

Polyaniline (PANI) base was protonated in aqueous solutions of an organic acid, 3-nitro-1,2,4-triazol-5(4H)-one (NTO). The temperature dependence of DC conductivity of PANI-NTO seems to correspond to the theory of variable range hopping (VRH) in three dimensions. The frequency dependence of AC conductivity also reflects the hopping nature of mobile charges. The activation energy for the polymers with protonation degree above 0.12 remains constant with increasing dopant concentration and DC conductivity. The value of this constant may correspond to the energy needed for the ionization of dopant counterion. The fit of the electric relaxation function to the stretched exponential function ϕ(t) = exp[−(t/τ)^β] gives the stretch parameter β about 0.35, which shows that the distribution of relaxation times is broad and indicates a high inhomogeneity in the distribution of a dopant.     

On the interpolation constants for variable Lebesgue spaces

For $\theta \in (0,1)$ and variable exponents $p_0(·),q_0(·)$ and $p_1(·),q_1(·)$ with values in [1, ∞], let the variable exponents $p_{\theta }(·),q_{\theta }(·)$ be defined by $$1/p_{\theta }(·):=(1-\theta )/p_0(·)+\theta /p_1(·),1/q_{\theta }(·):=(1-\theta )/q_0(·)+\theta /q_1(·).$$ The Riesz–Thorin–type interpolation theorem for variable Lebesgue spaces says that if a linear operator T acts boundedly from the variable Lebesgue space $L^{p_j(·)}$ to the variable Lebesgue space $L^{q_j(·)}$ for $j=0,1$, then $${\parallel T\parallel }_{L^{p_{\theta }(·)}\to L^{q_{\theta }(·)}}\le {C\parallel T\parallel }_{L^{p_0(·)}\to L^{q_0(·)}}^{1-\theta }{\parallel T\parallel }_{L^{p_1(·)}\to L^{q_1(·)}}^{\theta },$$ where C is an interpolation constant independent of T. We consider two different modulars ${\varrho }^{\max }(·)$ and ${\varrho }^{\mathrm{sum}}(·)$ generating variable Lebesgue spaces and give upper estimates for the corresponding interpolation constants C_max and C_sum, which imply that $C_{\max }\le 2$ and $C_{\mathrm{sum}}\le 4$, as well as, lead to sufficient conditions for $C_{\max }=1$ and $C_{\mathrm{sum}}=1$. We also construct an example showing that, in many cases, our upper estimates are sharp and the interpolation constant is greater than one, even if one requires that $p_j(·)=q_j(·)$, $j=0,1$ are Lipschitz continuous and bounded away from one and infinity (in this case, ${\varrho }^{\max }(·)={\varrho }^{\mathrm{sum}}(·)$).