Class Of Transformations Research Articles

Multiple Stacks of Rotated Metal Strip Gratings for High-Gain Bandwidth Enhancement and Gain Control of Overlying Dipoles—Analysis by Asymptotic Strips Boundary Conditions

As an amenable and efficient alternative to formulaically cumbersome and computationally demanding full-wave modal approaches, the herein analytical method uses the asymptotic strips boundary conditions along with classical vector potentials and coordinate transformations to treat multiple stacks of rotated metal strip gratings with general dielectric layers between them. For all cases, either with conducting terminal planes on just one side, on both, or none at all, solutions to plane-wave illuminated and/or modal dispersion eigenvalue problems are all obtainable. With the additional degrees of parametric freedom afforded by the angles of rotation between gratings, not only may wider ranges of special properties such as artificial surface impedances be achieved at fixed frequencies, they can also be reconfigured by the rotation of the gratings, being a simple, single-sweep-type mechanical motion, as opposed to electronic means entailing complex networks and intricate circuitries. In addition to the presentation of the formulation details and validation results, this article demonstrates the importance of multiple stacks of rotated strip gratings in widening the otherwise compromised bandwidths of artificial magnetic conductor (AMC) surface characteristics subjected to strict reflection-phase criterion for preserving high maximal broadside gains of overlying prostrate dipole antennas as well as attaining full-range gain control. Prototypes are manufactured and measured with a good agreement with theory.

Связь обратного преобразования Шура обобщённого класса Неванлинны с рациональными матричными функциями специального вида

In this paper we consider classical Schur transformation and inverse Schur transformation for generalized Nevanlinna functions.

One-Loop effective action approach to quantum MHV theory

It is well known that the MHV action, i.e. the action containing all the maximally helicity violating vertices, is alone not sufficient for loop computations. In order to develop loop contributions systematically and to ensure that there are no missing terms, we propose to formulate the quantum MHV action via one-loop effective action approach. The quadratic field fluctuations in the light cone Yang-Mills theory are explicitly integrated, followed by the classical canonical field transformation. We test the approach by calculating one loop (++++) and (+++) amplitudes, i.e. amplitudes that cannot be calculated from ordinary MHV action. Such an approach can be further used to unambiguously define loop corrections in other theories related to Yang-Mills theory by field transformations.

Prediction of the far field radiated by a flat antenna under test from a reduced set of near‐field bi‐polar measurements

In this article, a bi-polar near-field-to-far-field (NFTFF) transformation with probe compensation, which is very convenient from the data reduction standpoint when characterising a flat antenna under test (AUT), is developed. It takes advantage from the non-redundant sampling representations of the electromagnetic fields to devise a sampling representation on the scanning plane, which requires the knowledge of the bi-polar NF samples at a reduced number of sampling points. To account for the AUT geometry, it properly adopts as modelling surface a disc having diameter equal to the largest size of such an AUT. This surface allows a more effective AUT modelling from the NF data reduction standpoint than the formerly proposed modelling surfaces for quasi-planar antennas (the oblate ellipsoid or the two-bowls), because, unlike these last, it has the capability to best fit the AUT geometry, thus reducing very significantly the involved volumetric redundancy. An ad hoc developed two-dimensional optimal sampling, interpolation formula is then employed to reconstruct the plane-rectangular NF data which would be necessary to execute the classical NFTFF transformation developed by Leach and Paris. Some results of numerical simulations and experimental proofs are reported to demonstrate the efficiency of the so developed technique.

Faeces traits as unifying predictors of detritivore effects on organic matter turnover

• Detritivores are diverse animals which role in soil processes is difficult to predict. • We argue that detritivore faeces characteristics may be promising effect traits. • Two case studies show that faeces traits predict organic matter turnover. • This could unify groups of animals so far separated between soil- and litter-feeding. In the last decade, our understanding of plant litter decomposition and soil organic matter formation substantially improved but critical blind spots remain. Particularly, the role of detritivores, i.e. soil animals that feed on litter and soil, is poorly understood and notoriously missing from biogeochemical models. This major gap results from methodological difficulties to isolate their effect and from the astonishing diversity of detritivorous organisms with few common features, thereby hampering the identification of general patterns. In this viewpoint, we propose that the characteristics of their faeces can predict detritivore effects on soil processes related to organic matter turnover across the large detritivore diversity. Indeed, faeces are common to all detritivores, and a large part of organic matter is transformed into faeces in many ecosystems. Two recent studies presented here showed that faeces characteristics are powerful predictors of the fate and turnover of this transformed organic matter. We suggest that faeces characteristics, such as water-holding capacity, size and spatial organisation of the faecal pellets and of their constituting particles, particulate organic matter connectivity, as well as the characteristics of dissolved organic matter in faecal pellets, are promising ‘effect traits’. By focusing on similar features rather than differences, this approach has the potential to break down barriers of this highly fragmented soil animal group, in particular between earthworms that are often studied as ecosystem engineers and classical litter transformers such as millipedes, woodlice, or snails. We discuss ways of tackling the complexity of using such traits, particularly regarding the composite determinism of faeces characteristics that are driven both by the detritivore identity and the ingested organic matter. Rigorous and hypothesis-based use of faeces characteristics as effect traits, including clear identification of studied processes, could allow integrating detritivores in our current understanding of organic matter turnover.

A Fast Fourier Transform for the Johnson Graph

The set X of k-subsets of an n-set has a natural graph structure where two k-subsets are neighbors if and only if the size of their intersection is \(k-1\). This is known as the Johnson graph. The symmetric group \(S_n\) acts on the space of complex functions on X and this space has a multiplicity-free decomposition as sum of irreducible representations of \(S_n\), so it has a well-defined Gelfand–Tsetlin basis up to scalars. The Fourier transform on the Johnson graph is defined as the change of basis matrix from the delta function basis to the Gelfand–Tsetlin basis. The direct application of this matrix to a generic vector requires \(\left( {\begin{array}{c}n\\ k\end{array}}\right) ^2\) arithmetic operations. We show that, in analogy with the classical Fast Fourier Transform on the discrete circle, this matrix can be factorized as a product of \(n-1\) orthogonal matrices, each one with at most two nonzero elements in each column. The factorization is based on the construction of \(n-1\) intermediate bases which are parametrized via the Robinson–Schensted insertion algorithm. This factorization shows that the number of arithmetic operations required to apply this matrix to a generic vector is bounded above by \(2(n-1) \left( {\begin{array}{c}n\\ k\end{array}}\right) \). We give an algorithm that constructs all these factors using at most \(289(n-1)\left( {\begin{array}{c}n\\ k\end{array}}\right) \) arithmetic operations. The coefficients of these matrices are rational numbers and the construction does not depend on numerical methods. Instead, they are obtained by solving small linear systems with integer coefficients derived from the Jucys–Murphy operators. In particular we avoid the use of square roots. As a consequence, we show that the problem of computing all the weights of the isotypic components of a given function can be solved in \(O(n \left( {\begin{array}{c}n\\ k\end{array}}\right) )\) operations, improving the previous bound \(O(k^2 \left( {\begin{array}{c}n\\ k\end{array}}\right) )\) when k asymptotically dominates \(\sqrt{n}\). The same improvement is achieved for the problem of computing the isotypic projection onto a single component.

Face Anti-Spoofing Using Transformers With Relation-Aware Mechanism

Face anti-spoofing (FAS) is important to secure face recognition systems. Deep learning has obtained great success in this area, however, most existing approaches fail to consider comprehensive relation-aware local representations of live and spoof faces. To address this issue, we propose a Transformer-based Face Anti-Spoofing (TransFAS) model to explore comprehensive facial parts for FAS. Besides the multi-head self-attention which explores relations among local patches in the same layer, we propose cross-layer relation-aware attentions (CRA) to adaptively integrate local patches from different layers. Furthermore, to effectively fuse hierarchical features, we explore the best hierarchical feature fusion (HFF) structure, which can capture the complementary information between low-level artifacts and high-level semantic features for the spoofing patterns. With these novel modules, TransFAS not only improves the generalization capability of the classical vision transformer, but also achieves SOTA performance on multiple benchmarks, demonstrating the superiority of the transformer-based model for FAS.

IMPROVING AGRICULTURAL PRODUCTION AND FOOD SECURITY UNDER CLIMATE CHANGE CONDITIONS

Climate change represents a major challenge for food security in the coming years, as it is causing a significant reduction of crop yields worldwide, primarily due to the increase in the intensity and frequency of drought periods andthe progressive salinisation of irrigated farmland. The best strategy to improve agricultural production appears to bethe development of drought and salt-tolerant crop cultivars. Intensive research and promising results in recent years show that this objective will be reached soon, applying classical breeding (supported by modern molecular tools) and plant genetic transformation. In addition, domestication and commercial cultivation of stress-tolerant wild species will also help increase food production. In the meantime, other strategies will contribute, even if more modestly, to enhance stress tolerance and improve crop yields in the frame of sustainable agriculture. They could include using 'new generation' controlled-release fertilisers to optimise plant nutrition or applying a collection of unrelated substances and beneficial microorganisms with activity as 'biostimulants'. In this paper, some examples of these approaches will be discussed, with reference to recent reviews for further reading.

CLIP THINKING AS A DRIVER OF MODERN EDUCATION

The article reveals the problems of modern schoolchildren and students’ new type of thinking, formed through the Internet dominant role in the information search and processing. Young people are in information noise conditions, while there are no tools to influence the information flow, the only way to avoid overwork is to perceive incoming information in fragments like in a clip. In this article the author made an attempt to consider comprehensively the phenomenon of clip thinking, to determine the factors contributing to its appearance in generation Z, to analyze the criteria of cognitive-perceptual activity of clip thinking. This kind of analysis is feasible because of the interdisciplinarity of the phenomenon under consideration. The obtained results clearly illustrate the situation of the negative clip thinking impact on the traditional education system, since it is not able to fully ensure the material qualitative perception by students. Experts in this field note the need to change the entire structure in an evolutionary way, not breaking the usual scheme, but supplementing it with effective tools that help activate the clip thinking constructive aspects, including multitasking, information received rapid processing, solving tasks with the various modalities’ involvement. The use of relevant techniques in the educational process, provided by the various mobile devices’ potential, allows students to be interested, to teach them to work systematically and logically on a problem, to analyze, synthesize and verify the information that they generate themselves. The basic platforms, according to the author’s opinion, can be game learning platforms variety that involve in the educational process not only standard sources of information - textbooks, but also mobile devices that work as a digital ecosystem that allows you to solve any task of activating the potential of clip thinking. In conclusion, it was realized that the process of the classical educational system transformation is dynamically but systematically changing under the influence of a new thought process of the modern digital generation.

Mem3DG: Modeling membrane mechanochemical dynamics in 3D using discrete differential geometry

Biomembranes adopt varying morphologies that are vital to cellular functions. Many studies use computational modeling to understand how various mechanochemical factors contribute to membrane shape transformations. Compared with approximation-based methods (e.g., finite element method [FEM]), the class of discrete mesh models offers greater flexibility to simulate complex physics and shapes in three dimensions; its formulation produces an efficient algorithm while maintaining coordinate-free geometric descriptions. However, ambiguities in geometric definitions in the discrete context have led to a lack of consensus on which discrete mesh model is theoretically and numerically optimal; a bijective relationship between the terms contributing to both the energy and forces from the discrete and smooth geometric theories remains to be established. We address this and present an extensible framework, Mem3DG, for modeling 3D mechanochemical dynamics of membranes based on discrete differential geometry (DDG) on triangulated meshes. The formalism of DDG resolves the inconsistency and provides a unifying perspective on how to relate the smooth and discrete energy and forces. To demonstrate, Mem3DG is used to model a sequence of examples with increasing mechanochemical complexity: recovering classical shape transformations such as 1) biconcave disk, dumbbell, and unduloid; and 2) spherical bud on spherical, flat-patch membrane; investigating how the coupling of membrane mechanics with protein mobility jointly affects phase and shape transformation. As high-resolution 3D imaging of membrane ultrastructure becomes more readily available, we envision Mem3DG to be applied as an end-to-end tool to simulate realistic cell geometry under user-specified mechanochemical conditions.

Computational Simulation by Phase Field: Martensite Transformation Kinetics and Variant Selection under External Fields

Tailoring martensite transformation is critical for improving the mechanical properties of advanced steels. To provide preliminary guidance for the control of martensite transformation behaviour using external fields by computational simulation method, the phase-field method was used to calculate the morphology evolution, kinetics, and variant selection of the martensite transformation under different loading modes and magnetic field intensities. The incubation, transformation, and stable stages of the three variants based on the Bain strain group were investigated using different kinetic curves. These results clearly indicate that both uniaxial tension and compression can greatly promote the formation of martensite during the transformation stage and cause an obvious preferred variant selection. In contrast, the different variants have relatively balanced forms under shearing conditions. In addition, the magnetic field is a gentler way to form a state with balanced variants than other techniques such as shearing. Additionally, all these simulation results are consistent with classical martensitic transformation theory and thermodynamic mechanism, which proves the rationality of this research. The aim of the present study was to provide qualitative guidance for the selection of external fields for microstructural improvement in advanced steels.

Manifold turnpikes, trims, and symmetries

Classical turnpikes correspond to optimal steady states which are attractors of infinite-horizon optimal control problems. In this paper, motivated by mechanical systems with symmetries, we generalize this concept to manifold turnpikes. Specifically, the necessary optimality conditions projected onto a symmetry-induced manifold coincide with those of a reduced-order problem defined on the manifold under certain conditions. We also propose sufficient conditions for the existence of manifold turnpikes based on a tailored notion of dissipativity with respect to manifolds. Furthermore, we show how the classical Legendre transformation between Euler–Lagrange and Hamilton formalisms can be extended to the adjoint variables. Finally, we draw upon the Kepler problem to illustrate our findings.

Integration of design and NMPC-based control for chemical processes under uncertainty: An MPCC-based framework

The use of nonlinear model predictive control (NMPC) for the integration of design and control remains as an open area of research. When NMPC is incorporated into the framework for design and control, this results into a bilevel problem formulation. The search of a solution for a bilevel problem is often carried out with the implementation of systematic iterative methodologies. In this work, we implement the classical KKT transformation strategy to transform the original bilevel problem for simultaneous design and NMPC-based control into a single-level dynamic optimization problem. This single-level formulation is referred to as a mathematical program with complementarity constraints (MPCC). Violations to constraint qualifications (CQs) are avoided through the implementation of several reformulation techniques. This facilitates the convergence of the MPCC for optimal design and control. The use of an MPCC-based formulation allows to fully incorporate the NMPC’s necessary conditions for optimality into the design problem as a set of algebraic constraints. Accordingly, the MPCC is solved as a conventional NLP, i.e., we avoid the use of decomposition or simplification methodologies for the solution of the bilevel problem. This guarantees optimality in the solution for integrated design and NMPC-based control. This strategy was implemented in three case studies involving small, medium-scale, and highly nonlinear systems to demonstrate the application of MPCCs for design and NMPC-based control under process disturbances and uncertainty.

Generalized Gauge Transformation with PT$PT$‐Symmetric Non‐Unitary Operator and Classical Correspondence of Non‐Hermitian Hamiltonian for a Periodically Driven System

AbstractThis paper demonstrates that the parity‐time ()‐symmetric non‐Hermitian Hamiltonian for a periodically driven system can be generated from a kernel Hamiltonian by a generalized gauge transformation. The kernel Hamiltonian is Hermitian and static, while the time‐dependent transformation operator has to be symmetric and non‐unitary in general. Biorthogonal sets of eigenstates appear necessarily as a consequence of the non‐Hermitian Hamiltonian. The wave functions and associated non‐adiabatic Berry phase for the nth eigenstate are obtained analytically. The classical version of the non‐Hermitian Hamiltonian becomes a complex function of canonical variables and time. The corresponding kernel Hamiltonian is derived with symmetric canonical‐variable transfer in the classical gauge transformation. Moreover, with the change of position‐momentum to angle‐action variables it is revealed that the non‐adiabatic Hannay's angle and Berry phase satisfy precisely the quantum‐classical correspondence, .

Analysis of the Operation of Cascade Current Transformers for Measurements of Short-Circuit Currents with a Non-Periodic Component with a Large Time Constant of Its Decay

Simulations of emergency states and tests of resistance of electrical devices to emergencies are performed in specialized high-power laboratories, the so-called short-circuit laboratories. For most electrical power devices, such measurements are required by international standards. The basic equipment of short-circuit testing laboratories consists of current transformers for measuring short-circuit currents. These transformers should not only enable the accurate conversion of sinusoidal currents—which is typical for conventional current transformers, but also asymmetrical short-circuit currents containing an aperiodic component, which classic current transformers cannot reproduce. Therefore, manufacturers and designers try to meet the market demands and design these special class 0.2 current transformers. To meet the high technical requirements, the field-circuit method with three-dimensional space–time analysis of electromagnetic fields was used during design, considering physical phenomena in ferromagnetic cores (i.e., hysteresis and eddy current losses) and the load of the secondary winding of the current transformer by the measurement system. The article presents simulations of secondary currents for the short-circuit current transformer model, and the results were confirmed by measurements and oscillograms of the currents flowing in the windings of the real model. The prototype of the designed short-circuit transformer meets the IEC/EN standard requirements. When measuring harmonic currents, the transformation errors meet the requirements of class 0.2. During the short-circuit current waveforms, the maximum instantaneous peak error does not exceed 1% of the error for all the subsequent maxima of the current waveform during the specified transient switching cycle. In comparison, the standard allows this error to be 10%.

A constitutive model for metallic glasses based on two-temperature nonequilibrium thermodynamics

We develop a new finite deformation constitutive model for metallic glass within the framework of irreversible nonequilibrium thermodynamics. To consider the intrinsically out-of-equilibrium characteristics of metallic glass, its total internal energy is divided into two weakly coupled configurational and kinetic subsystems, and configurational temperature coupling with configurational degrees of freedom is introduced as a thermodynamic state variable to characterize the evolution of the disordered structure. Furthermore, the classical shear transformation zone theory is extended by reasonably considering the reverse shear transformation as a form of the relaxation of the strain field, which is stored in the elastic matrix and produced by the constraint of the matrix on shear transformation. With the help of the finite element implementation for the new model, the effectiveness of the proposed model is validated by comparing the modeling stress–strain responses of the macroscopic deformations under different temperatures and strain rates with the experimental results, and the utility of the model for predicting the shear banding behavior of metallic glasses is examined as well. The results therefore show that the constructed constitutive model can not only effectively predict the deformations of metallic glass under different ambient temperatures and applied strain rates, but also reasonably explain the mechanisms of deformation mode evolution and shear band formation.

CRISPR/Cas9-Mediated Mutagenesis of Abdominal-A and Ultrabithorax in the Asian Corn Borer, Ostrinia furnacalis.

Simple SummaryHomeotic genes encode transcription factors that coordinated the anatomical structure formation during the early embryonic development of organisms. In this study, we functionally characterized two homeotic genes, Abdominal-A (Abd-A) and Ultrabithorax (Ubx), in the Asian corn borer, Ostrinia furnacalis (a maize pest that has devastated the Asia-Pacific region) by using a CRISPR/Cas9 genome editing system. Our results show that the mutagenesis of OfAbd-A and OfUbx led to severe morphological defects in O. furnacalis, which included fused segments and segmental twist during the larval stage, and hollowed and incision-like segments during the pupal stage in OfAbd-A mutants, as well as defects in the wing-pad development in pupal and adult OfUbx mutants. Overall, knocking out Abd-A and Ubx in O. furnacalis resulted in the embryonic lethality to, and pleiotropic impact on, other homeotic genes. This study not only confirms the conserved body planning functions in OfAbd-A and OfUbx, but it also strengthens the control implications of these homeotic genes for lepidopteran pests.(1) Background: Abdominal-A (Abd-A) and Ultrabithorax (Ubx) are homeotic genes that determine the identity and morphology of the thorax and abdomen in insects. The Asian corn borer, Ostrinia furnacalis (Guenée) (Lepidoptera: Pyralidae), is a devastating maize pest throughout Asia, the Western Pacific, and Australia. Building on previous knowledge, we hypothesized that the knockout of Abd-A and Ubx would disrupt the abdominal body planning in O. furnacalis. (2) Methods: CRISPR/Cas9-targeted mutagenesis was employed to decipher the functions of these homeotic genes. (3) Results: Knockout insects demonstrated classical homeotic transformations. Specifically, the mutagenesis of OfAbd-A resulted in: (1) Fused segments and segmental twist during the larval stage; (2) Embryonic lethality; and (3) The pleiotropic upregulation of other homeotic genes, including Lab, Pd, Dfd, Antp, and Abd-B. The mutagenesis of OfUbx led to: (1) Severe defects in the wing pads, which limited the ability of the adults to fly and mate; (2) Female sterility; and (3) The pleiotropic upregulation of other homeotic genes, including Dfd, Abd-B, and Wnt1. (4) Conclusions: These combined results not only support our hypothesis, but they also strengthen the potential of using homeotic genes as molecular targets for the genetic control of this global insect pest.

Direct numerical simulation of hypersonic turbulent boundary layers: effect of spatial evolution and Reynolds number

Direct numerical simulations (DNS) are performed to investigate the spatial evolution of flat-plate zero-pressure-gradient turbulent boundary layers over long streamwise domains ( ${>}300\delta _i$ , with $\delta _i$ the inflow boundary-layer thickness) at three different Mach numbers, $2.5$ , $4.9$ and $10.9$ , with the surface temperatures ranging from quasiadiabatic to highly cooled conditions. The settlement of turbulence statistics into a fully developed equilibrium state of the turbulent boundary layer has been carefully monitored, either based on the satisfaction of the von Kármán integral equation or by comparing runs with different inflow turbulence generation techniques. The generated DNS database is used to characterize the streamwise evolution of multiple important variables in the high-Mach-number, cold-wall regime, including the skin friction, the Reynolds analogy factor, the shape factor, the Reynolds stresses, and the fluctuating wall quantities. The data confirm the validity of many classic and newer compressibility transformations at moderately high Reynolds numbers (up to friction Reynolds number $Re_\tau \approx 1200$ ) and show that, with proper scaling, the sizes of the near-wall streaks and superstructures are insensitive to the Mach number and wall cooling conditions. The strong wall cooling in the hypersonic cold-wall case is found to cause a significant increase in the size of the near-wall turbulence eddies (relative to the boundary-layer thickness), which leads to a reduced-scale separation between the large and small turbulence scales, and in turn to a lack of an outer peak in the spanwise spectra of the streamwise velocity in the logarithmic region.

New cases of Hankel operator diagonalization

We obtain some new cases of diagonalization of Hankel operator on the semiaxis. The kernels of these operators contain hyperbolic functions. The integral transformations diagonalizing these operators are a composition of the classical Mehler-Fock transformations, sine and cosine Fourier transforms and some unitary operator. The latter is written out explicitly.

STRATEGIC MANAGEMENT IN ECOSYSTEMS: ANALYSIS OF THE RUSSIAN EXPERIENCE

Ecosystems as new organizational forms of business, whose activity generates changes in the theory and practice of management, have become a significant phenomenon of the modern economy. The article discusses the features of the strategy development of ecosystems based on digital platforms, the typology of strategies and the directions of classical approaches transformation to the strategic development of ecosystem players. The research methodology includes the analysis of scientific approaches within the framework of the emerging ecosystem theory as well as the systematization of the national digital ecosystems’ practice based on the analysis of real situations from various spheres of Russian business. As a result of the analytical study, the multi-vector strategies of Russian ecosystems are described; the dominant directions of development in transaction ecosystems and decision ecosystems are identified and systematized on the basis of the Ansoff matrix. The directions of transformation of traditional methods and tools of strategic management in a broad context are revealed from the standpoint of market and intra-ecosystem interactions. The obtained results contribute to the urgent scientific discussions concerning the prospects and limitations of the digital ecosystems development, changes in the nature and models of competition, as well as the problems of traditional management methods transformation in the digital economy.