Drug-Induced Phase Separation in Polyelectrolyte Microgels

Polyelectrolyte microgels may undergo volume phase transition upon loading and the release of amphiphilic molecules, a process important in drug delivery. The new phase is “born” in the outermost gel layers, whereby it grows inward as a shell with a sharp boundary to the “mother” phase (core). The swelling and collapse transitions have previously been studied with microgels in large solution volumes, where they go to completion. Our hypothesis is that the boundary between core and shell is stabilized by thermodynamic factors, and thus that collapsed and swollen phases should be able to also coexist at equilibrium. We investigated the interaction between sodium polyacrylate (PA) microgel networks (diameter: 400–850 µm) and the amphiphilic drug amitriptyline hydrochloride (AMT) in the presence of NaCl/phosphate buffer of ionic strength (I) 10 and 155 mM. We used a specially constructed microscopy cell and micromanipulators to study the size and internal morphology of single microgels equilibrated in small liquid volumes of AMT solution. To probe the distribution of AMT micelles we used the fluorescent probe rhodamine B. The amount of AMT in the microgel was determined by a spectrophotometric technique. In separate experiments we studied the binding of AMT and the distribution between different microgels in a suspension. We found that collapsed, AMT-rich, and swollen AMT-lean phases coexisted in equilibrium or as long-lived metastable states at intermediate drug loading levels. In single microgels at I = 10 mM, the collapsed phase formed after loading deviated from the core-shell configuration by forming either discrete domains near the gel boundary or a calotte shaped domain. At I = 155 mM, single microgels, initially fully collapsed, displayed a swollen shell and a collapsed core after partial release of the AMT load. Suspensions displayed a bimodal distribution of swollen and collapsed microgels. The results support the hypothesis that the boundary between collapsed and swollen phases in the same microgel is stabilized by thermodynamic factors.

Coefficient Bounds of Kamali-Type Starlike Functions Related with a Limacon-Shaped Domain

In this article, we familiarize a subclass of Kamali-type starlike functions connected with limacon domain of bean shape. We examine certain initial coefficient bounds and Fekete-Szegö inequalities for the functions in this class. Analogous results have been acquired for the functions f − 1 and ξ / f ξ and also found the upper bound for the second Hankel determinant a 2 a 4 − a 3 2 .

Corner states in a second-order mechanical topological insulator

Demonstration of topological boundary modes in elastic systems has attracted a great deal of attention over the past few years due to its unique protection characteristic. Recently, second-order topological insulators have been proposed in manipulating the topologically protected localized states emerging only at corners. Here, we numerically and experimentally study corner states in a two-dimensional phononic crystal, namely a continuous elastic plate with embedded bolts in a hexagonal pattern. We create interfacial corners by adjoining trivial and non-trivial topological configurations. Due to the rich interaction between the bolts and the continuous elastic plate, we find a variety of corner states of and devoid of topological origin. Strikingly, some of the corner states are not only highly-localized but also tunable. Taking advantage of this property, we experimentally demonstrate asymmetric corner localization in a Z-shaped domain wall. This finding could create interest in exploration of tunable corner states for the use of advanced control of wave localization.

Momentum space toroidal moment in a photonic metamaterial

Berry curvature, the counterpart of the magnetic field in the momentum space, plays a vital role in the transport of electrons in condensed matter physics. It also lays the foundation for the emerging field of topological physics. In the three-dimensional systems, much attention has been paid to Weyl points, which serve as sources and drains of Berry curvature. Here, we demonstrate a toroidal moment of Berry curvature with flux approaching to π in judiciously engineered metamaterials. The Berry curvature exhibits a vortex-like configuration without any source and drain in the momentum space. Experimentally, the presence of Berry curvature toroid is confirmed by the observation of conical-frustum shaped domain-wall states at the interfaces formed by two metamaterials with opposite toroidal moments.

The first initial-boundary value problem of parabolic Monge–Ampère equations outside a bowl-shaped domain

In this paper, we study the parabolic Monge–Ampère equations $-u_{t}\det (D^{2}u)=g$ − u t det ( D 2 u ) = g outside a bowl-shaped domain with g being the perturbation of $g_{0}(|x|)$ g 0 ( | x | ) at infinity. Under the weaker conditions compared with the problem outside a cylinder, we obtain the existence and uniqueness of viscosity solutions with asymptotic behavior for the first initial-boundary value problem by using the Perron method.

Sharp Bounds of the Coefficient Results for the Family of Bounded Turning Functions Associated with a Petal-Shaped Domain

The goal of this article is to determine sharp inequalities of certain coefficient-related problems for the functions of bounded turning class subordinated with a petal-shaped domain. These problems include the bounds of first three coefficients, the estimate of Fekete-Szegö inequality, and the bounds of second- and third-order Hankel determinants.

COMPUTER PREDICTION OF TECHNOLOGICAL REGIMES OF RAPID CONE-SHAPED ADSORPTION FILTERS WITH CHEMICAL REGENERATION OF HOMOGENEOUS POROUS LOADS

Mathematical models for predicting technological regimes of filtration (water purification from the present impurities), backwashing, chemical regeneration and direct washing of rapid cone-shaped adsorption filters, taking into account the influence of temperature effects on the internal mass transfer kinetics at constant rates of the appropriate regimes, are formulated. Algorithms for numerical-asymptotic approximations of solutions of the corresponding nonlinear singularly perturbed boundary value problems for a model cone-shaped domain bounded by two equipotential surfaces and a flow surface are obtained. The proposed models in the complex allow computer experiments to be conducted to investigate the change of impurity concentrations in the filtration flow and on the surface of the load adsorbent, temperature of the filtration flow, filtration coefficient and active porosity along the filter height due to adsorption and desorption processes, and on their basis, to predict a good use of adsorbents and increase the protective time of rapid cone-shaped adsorption filters with chemical regeneration of homogeneous porous loads.

The Pohozaev-type inequalities and their applications for a kind of elliptic equation (system)

In this paper, we first derive a new kind of Pohozaev-type inequalities for p-Laplacian equations in a more general class of non-star-shaped domains, and then we take two examples and their graphs to explain the shape of the new kind of the non-star-shaped domain. At last, we extend the results of Pohozaev-type inequalities to elliptic systems, which are used to derive the nonexistence of positive solutions of this type of systems in the non-star-shaped domains. On this basis, we also discuss the existence of positive solutions of a kind of elliptic systems with double critical growth.