Oligomeric approach to 2D materials modeling

Oligomeric approach has been originally developed to study electronic properties of conjugated polymers. This approach allows to access electronic properties of 1D systems otherwise difficult to calculate. We successfully extended this method to study electronic properties of 2D materials. In this review we summarize our recent work in this area. It has been established that large graphene nanoflake possess multiconfigurational singlet or even high spin ground state. Doping of 2D systems has also been explored and it has been demonstrated that doping allows to tune their electronic properties, including ionization potentials, electron affinities, reorganization energies and the very nature of the ground state. The electronic properties of novel 2D allotropies of carbon, phosphorus, germanium and silicon have been studied as well as their complexes with Li. Heterostructures, of different 2D allotropies are readily formed. This is an alternative method for tuning of their electronic properties.

Observability and Geometric Approach of 2D Hybrid Systems

A connection is emphasized between two branches of the Systems Theory, namely the Geometric Approach and 2D Systems, with a special regard to the concept of observability. An algorithm is provided which determines the maximal subspace which is invariant with respect to two commutative matrices and which is included in a given subspace. Observability criteria are obtained for a class of 2D systems by using a suitable 2D observability Gramian and some such criteria are derived for LTI 2D systems, as well as the geometric characterization of the subspace of unobservable states. The presented algorithm is applied to determine this subspace.

Overactivated transport in the localized phase of the superconductor-insulator transition

Beyond a critical disorder, two-dimensional (2D) superconductors become insulating. In this Superconductor-Insulator Transition (SIT), the nature of the insulator is still controversial. Here, we present an extensive experimental study on insulating NbxSi1−x close to the SIT, as well as corresponding numerical simulations of the electrical conductivity. At low temperatures, we show that electronic transport is activated and dominated by charging energies. The sample thickness variation results in a large spread of activation temperatures, fine-tuned via disorder. We show numerically and experimentally that this originates from the localization length varying exponentially with thickness. At the lowest temperatures, there is an increase in activation energy related to the temperature at which this overactivated regime is observed. This relation, observed in many 2D systems shows that conduction is dominated by single charges that have to overcome the gap when entering superconducting grains.

Light-induced electron pairing in two-dimensional systems

The mechanism of electron pairing induced by a circularly polarized off-resonant electromagnetic field is suggested and examined theoretically for various two-dimensional (2D) nanostructures. Particularly, it is demonstrated that such a pairing can exist in 2D systems containing charge carriers with different effective masses. As a result of the pairing, the optically induced hybrid Bose-Fermy system appears. The elementary excitation in the system are analyzed and the possible Bose-Einstein condensation of the paired electrons and the related light-induced superconductivity are discussed.

New relaxed stability and stabilization conditions for both discrete and differential linear repetitive processes

The paper develops new results on stability analysis and stabilization of linear repetitive processes. Repetitive processes are a distinct subclass of two-dimensional (2D) systems, whose origins are in the modeling for control of mining and metal rolling operations. The reported systems theory for them has been applied in other areas such iterative learning control, where, uniquely among 2D systems based designs, experimental validation results have been reported. This paper uses a version of the Kalman–Yakubovich–Popov Lemma to develop new less conservative conditions for stability in terms of linear matrix inequalities, with an extension to control law design. Differential and discrete dynamics are analysed in an unified manner, and supporting numerical examples are given.

3D cell culture technology – a new insight into in vitro research – a review

Most in vitro cell-based research is based on two-dimensional (2D) systems where growth and development take place on a flat surface, which does not reflect the natural environment of the cells. The imperfection and limitations of culture in 2D systems eventually led to the creation of three-dimensional (3D) culture models that more closely reproduce the actual conditions of physiological cell growth. Since the inception of 3D culture technology, many culture models have been developed, such as technologies of multicellular spheroids, organoids, and organs on chips in the technology of scaffolding, hydrogels, bio-printing and liquid media. In this review we will focus on the advantages and disadvantages of the 2D vs. 3D cell cultures technologies. We will also try to sum up available 3D cultures systems and materials for building 3D scaffolds.

Extreme Poisson’s Ratios of Honeycomb, Re-Entrant, and Zig-Zag Crystals of Binary Hard Discs

Two-dimensional (2D) crystalline structures based on a honeycomb geometry are analyzed by computer simulations using the Monte Carlo method in the isobaric-isothermal ensemble. The considered crystals are formed by hard discs (HD) of two different diameters which are very close to each other. In contrast to equidiameter HD, which crystallize into a homogeneous solid which is elastically isotropic due to its six-fold symmetry axis, the systems studied in this work contain artificial patterns and can be either isotropic or anisotropic. It turns out that the symmetry of the patterns obtained by the appropriate arrangement of two types of discs strongly influences their elastic properties. The Poisson’s ratio (PR) of each of the considered structures was studied in two aspects: (a) its dependence on the external isotropic pressure and (b) in the function of the direction angle, in which the deformation of the system takes place, since some of the structures are anisotropic. In order to accomplish the latter, the general analytic formula for the orientational dependence of PR in 2D systems was used. The PR analysis at extremely high pressures has shown that for the vast majority of the considered structures it is approximately direction independent (isotropic) and tends to the upper limit for isotropic 2D systems, which is equal to +1. This is in contrast to systems of equidiameter discs for which it tends to 0.13, i.e., a value almost eight times smaller.