Time-periodic corner states from Floquet higher-order topology

The recent discoveries of higher-order topological insulators (HOTIs) have shifted the paradigm of topological materials, previously limited to topological states at boundaries of materials, to include topological states at boundaries of boundaries, such as corners. So far, all HOTI realisations have been based on static systems described by time-invariant Hamiltonians, without considering the time-variant situation. There is growing interest in Floquet systems, in which time-periodic driving can induce unconventional phenomena such as Floquet topological phases and time crystals. Recent theories have attempted to combine Floquet engineering and HOTIs, but there has been no experimental realisation so far. Here we report on the experimental demonstration of a two-dimensional (2D) Floquet HOTI in a three-dimensional (3D) acoustic lattice, with modulation along a spatial axis serving as an effective time-dependent drive. Acoustic measurements reveal Floquet corner states with double the period of the underlying drive; these oscillations are robust, like time crystal modes, except that the robustness arises from topological protection. This shows that space-time dynamics can induce anomalous higher-order topological phases unique to Floquet systems.

Toward a Logic of the Organism: A Process Philosophical Consideration

Mathematical models applied in contemporary theoretical and systems biology are based on some implicit ontological assumptions about the nature of organisms. This article aims to show that real organisms reveal a logic of internal causality transcending the tacit logic of biological modeling. Systems biology has focused on models consisting of static systems of differential equations operating with fixed control parameters that are measured or fitted to experimental data. However, the structure of real organisms is a highly dynamic process, the internal causality of which can only be captured by continuously changing systems of equations. In addition, in real physiological settings kinetic parameters can vary by orders of magnitude, i.e., organisms vary the value of internal quantities that in models are represented by fixed control parameters. Both the plasticity of organisms and the state dependence of kinetic parameters adds indeterminacy to the picture and asks for a new statistical perspective. This requirement could be met by the arising Biological Statistical Mechanics project, which promises to do more justice to the nature of real organisms than contemporary modeling. This article concludes that Biological Statistical Mechanics allows for a wider range of organismic ontologies than does the tacitly followed ontology of contemporary theoretical and systems biology, which are implicitly and explicitly based on systems theory.

Сonstruction of regression models for developing the technology to obtain tablets based on medicinal ginger

Scientific research in pharmacy, due to their multifactorial nature, is closely related to modeling of complex static systems. For this purpose, the so-called “input-output” mathematical models, which are built based on the results of the experiment, are widely used. Modeling of static systems based on the experimental data requires the solution of three interrelated tasks: planning of the experiment and its implementation; identification of the model structure and its parameters; approximation, if necessary, of a complex model to a simpler mathematical description.

Study of The Biodegradation of Poly (3- Hydroxybutyrate) (PHB) and High-Density Polyethylene (HDPE) by Microorganisms from the Sea waters of the Atlantic Coast of Brazil

The objective of this study was to evaluate the biodegradation of Poly (hydroxybutyrate) (PHB) and high-density polyethylene (HDPE) in static systems, using as fluid the seawater of the Coastal Region of the State of Pernambuco (Brazil). The physical and chemical modifications of the polymers, as a function of biodegradation, were evaluated by Fourier transform infrared spectroscopy (FTIR), mechanical tensile assay, differential scanning calorimetry (DSC), gravimetric test, and microbiological analysis. Through the FTIR, it was possible to observe in the PHB a decrease of 23.22% in the carbonyl index for the crystalline phase and 32.30% in the amorphous phase after 180 days, which evidences the effect of the biodegradation present. The mechanical properties of PHB were altered with biodegradation, but the thermal properties remained. During the gravimetric tests, there was a reduction in mass and consequently higher degradation rates for PHB, which is corroborated by the microbiological tests of the system. All characterizations demonstrated that the surface of the HDPE is less susceptible to biofilm formation and, consequently, to the enzymatic action of microorganisms. After 180 days of immersion, no significant microbiological degradation was observed in the HDPE, except for some abiotic alterations.

Formation of information support for the development of freight transportation of JSC “Ukrzaliznytsya”

A methodical approach to the formation of indicators of the information base of management decisions on the development of freight JSC “Ukrzaliznytsia”, which consists in calculating the taxonomy of the level of development of freight by substantiating systems and its elements: eighteen static systems, elements of which are six regional railways; seven dynamic systems – regional branches and in general JSC “Ukrzaliznytsia”. A spatial and temporal comparison of the development of freight transportation of selected systems is carried out. The taxonomy index is calculated on the basis of five indicators of freight traffic for the period 2002-2019. The analysis of static systems made it possible to identify the uneven development of freight transportation of regional branches of JSC “Ukrzaliznytsia” for the studied 18 years. The temporal comparison of the levels of development of freight traffic by each railway in particular also showed their instability. Fluctuations are observed in the last three years of the study period. In 2018, JSC “Ukrzaliznytsia” demonstrated the lowest level of freight transportation development for the entire analyzed year 2002-2019. It was established that both external and internal factors caused the negative impact on rail transportation, in particular: the economic crisis of 2014-2015; military action in eastern Ukraine; ineffective management at different levels of government. The introduction of quarantine measures due to the COVID-19 pandemic caused unprofitable and deteriorating financial and economic performance of JSC Ukrzaliznytsia, and its six regional branches in 2020, in particular, revenues from freight transportation decreased by 10.3% compared to 2019, and net loss amounted to UAH 11.9 billion. Implementing the anti-crisis plan by the management of JSC Ukrzaliznytsia and the improvement of operational work in the freight segment has yielded some positive results. However, for the effective planning and management decisions in the field of freight transportation an important component is the proper formation of an information base. The proposed methodological approach will serve as an effective tool not only in the management of the freight segment of individual regional branches or enterprises in particular, but also the economic development of JSC “Ukrzaliznytsia” in general and can be used by other large companies.

Polynomial filter diagonalization of large Floquet unitary operators

Periodically driven quantum many-body systems play a central role for our understanding of nonequilibrium phenomena. For studies of quantum chaos, thermalization, many-body localization and time crystals, the properties of eigenvectors and eigenvalues of the unitary evolution operator, and their scaling with physical system size LL are of interest. While for static systems, powerful methods for the partial diagonalization of the Hamiltonian were developed, the unitary eigenproblem remains daunting. % In this paper, we introduce a Krylov space diagonalization method to obtain exact eigenpairs of the unitary Floquet operator with eigenvalue closest to a target on the unit circle. Our method is based on a complex polynomial spectral transformation given by the geometric sum, leading to rapid convergence of the Arnoldi algorithm. We demonstrate that our method is much more efficient than the shift invert method in terms of both runtime and memory requirements, pushing the accessible system sizes to the realm of 20 qubits, with Hilbert space dimensions \geq 10^6≥106.