Recent progress in silicon-based biologically sensitive field-effect devices

Biologically sensitive field-effect devices (BioFEDs) advantageously combine the electronic field-effect functionality with the (bio)chemical receptor's recognition ability for (bio)chemical sensing. In this review, basic and widely applied device concepts of silicon-based BioFEDs (ion-sensitive field-effect transistor, silicon nanowire transistor, electrolyte-insulator-semiconductor capacitor, and light-addressable potentiometric sensor) are presented, and recent progress (from 2019 to early 2021) is discussed. One of the main advantages of BioFEDs is the label-free sensing principle enabling them to detect a large variety of biomolecules and bioparticles by their intrinsic charge. The review encompasses applications of BioFEDs for the label-free electrical detection of clinically relevant protein biomarkers, DNA molecules and viruses, enzyme–substrate reactions as well as recording of the cell acidification rate (as an indicator of cellular metabolism) and the extracellular potential.     

Field‐Effect Nanoparticle‐Based Glucose Sensor on a Chip: Amplification Effect of Coimmobilized Redox Species

A capacitive EIS (electrolyte‐insulator‐semiconductor) structure was modified with gold nanoparticles together with glucose oxidase and used as field‐effect‐based glucose biosensor using the constant capacitance mode. Co‐immobilization of ferrocene redox species resulted in a two‐fold increase of the biosensor sensitivity. The effect was explained by the hydrogen peroxide‐mediated oxidation of ferrocene resulting in a pool of charged species at the interface increasing the sensor response towards glucose. The studied approach was suggested as a general means to amplify signals from Si chip‐based field‐effect enzyme biosensors.     

X‐ray focusing by the system of refractive lens(es) placed inside asymmetric channel‐cut crystals

An X‐ray one‐dimensionally focusing system, a refracting–diffracting lens (RDL), composed of Bragg double‐asymmetric‐reflecting two‐crystal plane parallel plates and a double‐concave cylindrical parabolic lens placed in the gap between the plates is described. It is shown that the focal length of the RDL is equal to the focal distance of the separate lens multiplied by the square of the asymmetry factor. One can obtain RDLs with different focal lengths for certain applications. Using the point‐source function of dynamic diffraction, as well as the Green function in a vacuum with parabolic approximation, an expression for the double‐diffracted beam amplitude for an arbitrary incident wave is presented. Focusing of the plane incident wave and imaging of a point source are studied. The cases of non‐absorptive and absorptive lenses are discussed. The intensity distribution in the focusing plane and on the focusing line, and its dependence on wavelength, deviation from the Bragg angle and magnification is studied. Geometrical optical considerations are also given. RDLs can be applied to focus radiation from both laboratory and synchrotron X‐ray sources, for X‐ray imaging of objects, and for obtaining high‐intensity beams. RDLs can also be applied in X‐ray astronomy.     

Propagation of Smallness and the Uniqueness of Solutions to Some Elliptic Equations in the Plane

In this paper we prove theorems on propagation of smallness and the uniqueness of solutions to some elliptic equations in the plane. We start with analogues of these theorems for harmonic functions and use their quasiinvariance under quasiconformal mappings as well as the connection of considered equations with such mappings.     

Poincaré Polynomial of Moduli Spaces of Framed Sheaves on (Stacky) Hirzebruch Surfaces

We perform a study of the moduli space of framed torsion-free sheaves on Hirzebruch surfaces by using localization techniques. We discuss some general properties of this moduli space by studying it in the framework of Huybrechts-Lehn theory of framed modules. We classify the fixed points under a toric action on the moduli space, and use this to compute the Poincaré polynomial of the latter. This will imply that the moduli spaces we are considering are irreducible. We also consider fractional first Chern classes, which means that we are extending our computation to a stacky deformation of a Hirzebruch surface. From the physical viewpoint, our results provide the mathematical framework for the counting of D4-D2-D0 branes bound states on total spaces of the bundles O_{\mathbb P¹}(-p){\mathcal {O}_{\mathbb {P}^1}(-p)} .     

Multiparameter Sensor Chip with Barium Strontium Titanate as Multipurpose Material

It is well known that biochemical and biotechnological processes are strongly dependent and affected by a variety of physico‐chemical parameters such as pH value, temperature, pressure and electrolyte conductivity. Therefore, these quantities have to be monitored or controlled in order to guarantee a stable process operation, optimization and high yield. In this work, a sensor chip for the multiparameter detection of three physico‐chemical parameters such as electrolyte conductivity, pH and temperature is realized using barium strontium titanate (BST) as multipurpose material. The chip integrates a capacitively coupled four‐electrode electrolyte‐conductivity sensor, a capacitive field‐effect pH sensor and a thin‐film Pt‐temperature sensor. Due to the multifunctional properties of BST, it is utilized as final outermost coating layer of the processed sensor chip and serves as passivation and protection layer as well as pH‐sensitive transducer material at the same time. The results of testing of the individual sensors of the developed multiparameter sensor chip are presented. In addition, a quasi‐simultaneous multiparameter characterization of the sensor chip in buffer solutions with different pH value and electrolyte conductivity is performed. To study the sensor behavior and the suitability of BST as multifunctional material under harsh environmental conditions, the sensor chip was exemplarily tested in a biogas digestate.     

Large-time geometric properties of solutions of the evolution p-Laplacian equation

We establish the behavior of the solutions of the degenerate parabolic equation

     

Some new monotonicity formulas and the singular set in the lower dimensional obstacle problem

We construct two new one-parameter families of monotonicity formulas to study the free boundary points in the lower dimensional obstacle problem. The first one is a family of Weiss type formulas geared for points of any given homogeneity and the second one is a family of Monneau type formulas suited for the study of singular points. We show the uniqueness and continuous dependence of the blowups at singular points of given homogeneity. This allows to prove a structural theorem for the singular set. Our approach works both for zero and smooth non-zero lower dimensional obstacles. The study in the latter case is based on a generalization of Almgren’s frequency formula, first established by Caffarelli, Salsa, and Silvestre. N. Garofalo is supported in part by NSF grant DMS-0701001. A. Petrosyan is supported in part by NSF grant DMS-0701015.