Uniform stabilization to equilibrium of a nonlinear fluid–structure interaction model

We consider uniform stability to a nontrivial equilibrium of a nonlinear fluid–structure interaction (FSI) defined on a two or three dimensional bounded domain. Stabilization is achieved via boundary and/or interior feedback controls implemented on both the fluid and the structure. The interior damping on the fluid combining with the viscosity effect stabilizes the dynamics of fluid. However, this dissipation propagated from the fluid alone is not sufficient to drive uniformly to equilibrium the entire coupled system. Therefore, additional interior damping on the wave component or boundary porous like damping on the interface is considered. A geometric condition on the interface is needed if only boundary damping on the wave is active. The main technical difficulty is the mismatch of regularity of hyperbolic and parabolic component of the coupled system. This is overcome by considering special multipliers constructed from Stokes solvers. The uniform stabilization result obtained in this article is global for the fully coupled FSI model.     

Global stability of humoral immunity virus dynamics models with nonlinear infection rate and removal

In this paper, we investigate the dynamical behavior of two nonlinear models for viral infection with humoral immune response. The first model contains four compartments; uninfected target cells, actively infected cells, free virus particles and B cells. The intrinsic growth rate of uninfected cells, incidence rate of infection, removal rate of infected cells, production rate of viruses, neutralization rate of viruses, activation rate of B cells and removal rate of B cells are given by more general nonlinear functions. The second model is a modification of the first one by including an eclipse stage of infected cells. We assume that the latent-to-active conversion rate is also given by a more general nonlinear function. For each model we derive two threshold parameters and establish a set of conditions on the general functions which are sufficient to determine the global dynamics of the models. By using suitable Lyapunov functions and LaSalle’s invariance principle, we prove the global asymptotic stability of the all equilibria of the models. We perform some numerical simulations for the models with specific forms of the general functions and show that the numerical results are consistent with the theoretical results.     

Nucleoside and oligonucleotide pyrene conjugates with 1,2,3-triazolyl or ethynyl linkers: synthesis,duplex stability,and fluorescence changes generated by the DNA-dye connector

Fluorescent nucleosides and oligonucleotides functionalized with pyrene were synthesized using ‘click’ chemistry or the Sonogashira cross-coupling reaction. The dye was connected to position-7 of 7-deaza-2′-deoxyguanosine or to the 2′-deoxyribofuranose moiety. Four different DNA-dye connectors with 1,2,3-triazolyl residues or triple bonds were constructed. Phosphoramidites of the pyrene conjugates (9, 14, 25) were prepared and used in solid-phase synthesis. Short linkers (2, 4) destabilize DNA, while long linkers (1) increased duplex stability. Nucleosides and oligonucleotides with single dye incorporations show linker dependent fluorescence. Linker dependent excimer emission with pyrenes in proximal positions was also observed. A ‘superchromophore’ formed by the 7-deaza-2′-deoxyguanosine ethynylpyrene conjugate shows strong red shifted fluorescence emission at 495 nm.     

Thermal Stability of Amorphous Solid Dispersions

Amorphous solid dispersion drug delivery systems (ASD DDS) were proved to be efficient for the enhancement of solubility and bioavailability of poorly water-soluble drugs. One of the major keys for successful preparation of ASD is the selection of appropriate excipients, mostly polymers, which have a crucial role in improving drug solubility and its physical stability. Even though, excipients should be chemically inert, there is some evidence that polymers can affect the thermal stability of active pharmaceutical ingredients (API). The thermal stability of a drug is closely related to the shelf-life of pharmaceutical products and therefore it is a matter of high pharmaceutical relevance. An overview of thermal stability of amorphous solids is provided in this paper. Evaluation of thermal stability of amorphous solid dispersion is perceived from the physicochemical perspective, from a kinetic (motions) and thermodynamic (energy) point of view, focusing on activation energy and fragility, as well all other relevant parameters for ASD design, with a glance on computational kinetic analysis of solid-state decomposition.     

Structural and anisotropic elastic properties of hexagonal MP (M = Ti,Zr, Hf) monophosphides determined by first-principles calculations

First-principles calculations were performed to investigate the structural properties, phase stabilities, elastic properties and thermal conductivities of MP (M = Ti, Zr, Hf) monophosphides. These monophosphides are thermodynamically and mechanically stable. Values for the bulk modulus B, shear modulus G, Young’s modulus E and Poisson’s ratio ν were calculated by Voigt–Reuss–Hill approximation. The mechanical anisotropy was discussed via several anisotropy indices and three-dimensional (3D) surface constructions. The order of elastic anisotropy is ZrP > HfP > TiP. The minimum thermal conductivities of these monophosphides were investigated using Clarke’s model and Cahill’s model. The results revealed that these monophosphides are suitable for use as thermal insulating materials and that their minimum thermal conductivities are anisotropic.     

Structure and stability of a silicon cluster on sequential doping with carbon atoms

SiC is a highly stable material in bulk. On the other hand, alloys of silicon and carbon at nanoscale length are interesting from both technological as well fundamental view point and are being currently synthesized by various experimental groups (Truong et. al., 2015 [26]). In the present work, we identify a well-known silicon cluster viz., Si₁₀ and dope it sequentially with carbon atoms. The evolution of electronic structure (spin state and the structural properties) on doping, the charge redistribution and structural properties are analyzed. It is interesting to note that the ground state SiC clusters prefer to be in the lowest spin state. Further, it is seen that carbon atoms are the electron rich centres while silicon atoms are electron deficient in every SiC alloy cluster. The carbon–carbon bond lengths in alloy clusters are equivalent to those seen in fullerene molecules. Interestingly, the carbon atoms tend to aggregate together with silicon atoms surrounding them by donating the charge. As a consequence, very few Si–Si bonds are noted with increasing concentrations of C atoms in a SiC alloy. Physical and chemical stability of doped clusters is studied by carrying out finite temperature behaviour and adsorbing O₂ molecule on Si₉C and Si₈C₂ clusters, respectively.     

Numerical study for the electrified instability of viscoelastic cylindrical dielectric fluid film surrounded by a conducting gas

The linear electrohydrodynamic cylindrical instability of annular Walters B^′${\mathrm{B}}^{\prime }$ viscoelastic dielectric fluid layer surrounded by a conducting gas in the presence of radial electric field is investigated. The obtained dispersion relation is found to be complicated and cannot be treated theoretically easily. Two limiting cases of interest are investigated, when the inertia is dominant, and when both the kinematic viscosity and viscoelasticity are high, and the corresponding new stability conditions are obtained for both cases. We solve the eigenvalue problem numerically using the continuation method which gives better results than the classical non-linear solvers such as Newton and Secant methods. It is found that the applied radial electric field has a dual role on the stability of the considered system, depending of the chosen wavenumbers range. Both the kinematic viscoelasticity and liquid depth are found to have stabilizing effects, while both the kinematic viscosity and surface tension have destabilizing effects on the considered system. The stability or instability breaks down for critical wavenumber values at which the growth rate vanishes. The behaviors of both the maximum growth rate and the corresponding dominant wavenumber are discussed in detail corresponding to the effect of all physical parameters. Finally a comparison between the results obtained here for Walters B^′${\mathrm{B}}^{\prime }$ viscoelastic fluids, and those obtained here too if the fluid is replaced by a Rivlin–Ericksen viscoelastic one is achieved. The limiting cases of absence of electric field and/or kinematic viscoelasticity are also investigated in detail.     

Hydromagnetic parametric resonance instability of two superposed conducting fluids in porous medium

Rayleigh–Taylor instability of a heavy fluid supported by a lighter one through porous medium, in the presence of a uniform, horizontal and oscillating magnetic field is studied. The fluids are taken as viscous (obeying Darcy's law), uniform, incompressible, and infinitely conducting. The amplitude of the oscillating part of the field is taken to be small compared with its steady part. The dispersion relation is obtained in the form of a third-order differential equation, with time as the independent variable and with periodic coefficients, for the vertical displacement of the surface of separation of the two fluids from its equilibrium position. The oscillatory magnetic field of frequency ω$\omega$ and steady part _H0$H_0$ has a stabilizing influence on a mode of disturbance which is unstable in a steady magnetic field of strength _H0$H_0$. It is found that the oscillatory magnetic field and porosity of the porous medium have stabilizing effects, while the medium permeability has a destabilizing influence on the considered system. For a constant value of any of these physical parameters, the system has been found to be unstable (for small wavenumbers) as well as stable afterwards after a definite wavenumber value. The marginal stability case of parametric resonance holds when _M1=_M2=0$M_1=M_2=0$ (and hence m=0$m=0$), in which the characteristic exponents, and the corresponding solutions for u$u$ break down, is also investigated in detail. It is found, to order ?$?$, that the effect of an oscillating magnetic field has no stabilizing influence on a disturbance which is marginally stable in the steady magnetic field; while to order ?²${?}^2$, and when the magnetic field oscillates, a resonance between this mode of disturbances and the oscillating field leads to instability when _ρ2>_ρ1${\rho }_2>{\rho }_1$. It is found also, in this resonant case, that all the constant or varied physical parameters, mentioned above, have destabilizing influences on the considered system. Finally, the other two resonance points appear in non-porous media (i.e., when m=±iω$m=\pm \mathrm{i}\omega$ and m=±2iω$m=\pm 2\mathrm{i}\omega$), are disappeared here due to the presence of the porous medium.