Finite Fragments Research Articles

A cloud model target damage effectiveness assessment algorithm based on spatio-temporal sequence finite multilayer fragments dispersion

To solve the problem of target damage assessment when fragments attack target under uncertain projectile and target intersection in an air defense intercept, this paper proposes a method for calculating target damage probability leveraging spatio-temporal finite multilayer fragments distribution and the target damage assessment algorithm based on cloud model theory. Drawing on the spatial dispersion characteristics of fragments of projectile proximity explosion, we divide into a finite number of fragments distribution planes based on the time series in space, set up a fragment layer dispersion model grounded in the time series and intersection criterion for determining the effective penetration of each layer of fragments into the target. Building on the precondition that the multilayer fragments of the time series effectively assail the target, we also establish the damage criterion of the perforation and penetration damage and deduce the damage probability calculation model. Taking the damage probability of the fragment layer in the spatio-temporal sequence to the target as the input state variable, we introduce cloud model theory to research the target damage assessment method. Combining the equivalent simulation experiment, the scientific and rational nature of the proposed method were validated through quantitative calculations and comparative analysis.

Mapping of Hückel zigzag carbon nanotubes onto independent polyene chains: Application to periodic nanotubes.

The electric polarizability and the spread of the total position tensors are used to characterize the metallic vs insulator nature of large (finite) systems. Finite clusters are usually treated within the open boundary condition formalism. This introduces border effects, which prevent a fast convergence to the thermodynamic limit and can be eliminated within the formalism of periodic boundary conditions. Recently, we introduced an original approach to periodic boundary conditions, named Clifford boundary conditions. It considers a finite fragment extracted from a periodic system and the modification of its topology into that of a Clifford torus. The quantity representing the position is modified in order to fulfill the system periodicity. In this work, we apply the formalism of Clifford boundary conditions to the case of carbon nanotubes, whose treatment results in a particularly simple zigzag geometry. Indeed, we demonstrate that at the Hückel level, these nanotubes, either finite or periodic, are formally equivalent to a collection of non-interacting dimerized linear chains, thus simplifying their treatment. This equivalence is used to describe some nanotube properties as the sum of the contributions of the independent chains and to identify the origin of peculiar behaviors (such as conductivity). Indeed, if the number of hexagons along the circumference is a multiple of three, a metallic behavior is found, namely a divergence of both the (per electron) polarizability and total position spread of at least one linear chain. These results are in agreement with those in the literature from tight-binding calculations.

Probabilistic weak bisimulation and axiomatization for probabilistic models

Recently a branching bisimilarity congruence has been established for randomized process models in a model independent approach. In this paper, we propose a probabilistic weak bisimilarity for randomized CCS based on the notion of weak ϵ-tree and show that it is a congruence. We also provide a complete axiomatization for the finite fragment of the language. Both the definition of weak bisimilarity and the proof of congruence respect model independency and thus can be easily generalized to a randomized extension of any interactive model.

Infinite-horizon risk-sensitive performance criteria for translation invariant networks of linear quantum stochastic systems

This paper is concerned with networks of identical linear quantum stochastic systems which interact with each other and external bosonic fields in a translation invariant fashion. The systems are associated with sites of a multidimensional lattice and are governed by coupled linear quantum stochastic differential equations (QSDEs). The block Toeplitz coefficients of these QSDEs are specified by the energy and coupling matrices which quantify the Hamiltonian and coupling operators for the component systems. We discuss the invariant Gaussian quantum state of the network when it satisfies a stability condition and is driven by statistically independent vacuum fields. A quadratic-exponential functional (QEF) is considered as a risk-sensitive performance criterion for a finite fragment of the network over a bounded time interval. This functional involves a quadratic function of dynamic variables of the component systems with a block Toeplitz weighting matrix. Assuming the invariant state, we study the spatio-temporal asymptotic rate of the QEF per unit time and per lattice site in the thermodynamic limit of unboundedly growing time horizons and fragments of the lattice. A spatio-temporal frequency-domain formula is obtained for the QEF rate in terms of two spectral functions associated with the real and imaginary parts of the invariant quantum covariance kernel of the network variables. A homotopy method and asymptotic expansions for evaluating the QEF rate are also discussed.

Nanodiamond islands confined between two graphene sheets as perspective 2D quantum materials

Based on direct space DFT PBE0/6-31G* electronic structure calculations, the structure and properties of nanodiamond islands confined between two finite graphene fragments (NDI-c2G) was proposed and theoretically explored. DFT simulations revealed that fusion of planar aromatic molecules with two parent graphene fragments may form either cubic or hexagonal allotropes of NDI-c2Gs lattices accompanied with formation of local corrugated sp3 sites with substituted dangling bonds embedded into graphene sublattices. It was shown that at the DFT level of theory, low distortion energies of NDI-c2Gs lattices are comparable or smaller than the energy of van-der-Waals interactions, which allows the NDI-c2G lattices to be stabilized by a support and finally synthesized. The Nuclear Independent Chemical Shift calculations, shows that in the vicinity of NDI regions, graphene lattices are estimated to be either low-, or anti-aromatic. Furthermore, the formation of NDI-c2Gs leads to localization of HOMO and LUMO states at different sites of the NDI-c2Gs lattices. The NDI-c2G regions with confined frontier orbitals can be considered as arrays of quantum dots isolated from each other by NDI scattering centres of 3.82 Å dimension. The results demonstrates that NDI-c2G should be considered as strongly-correlated entangled hybrid quantum dots which may form extended quantum ensembles with great potential for advanced quantum applications.

From affine A4 to affine H2: group-theoretical analysis of fivefold symmetric tilings.

The projections of lattices may be used as models of quasicrystals, and the particular affine extension of the H2 symmetry as a subgroup of A4, discussed in this work, presents a different perspective on fivefold symmetric quasicrystallography. Affine H2 is obtained as the subgroup of affine A4. The infinite discrete group with local dihedral symmetry of order 10 operates on the Coxeter plane of the root and weight lattices of A4 whose Voronoi cells tessellate the 4D Euclidean space possessing the affine A4 symmetry. Facets of the Voronoi cells of the root and weight lattices are identified. Four adjacent rhombohedral facets of the Voronoi cell V(0) of A4 project into the decagonal orbit of H2 as thick and thin rhombuses where long diagonals of the rhombohedra serve as reflection line segments of the reflection operators of H2. It is shown that the thick and thin rhombuses constitute the finite fragments of the tiles of the Coxeter plane with the action of the affine H2 symmetry. Projection of the Voronoi cell of the weight lattice onto the Coxeter plane tessellates the plane with four different tiles: thick and thin rhombuses with different edge lengths obtained from the projection of the square faces and two types of hexagons obtained from the projection of the hexagonal faces of the Voronoi cell. The structure of the local dihedral symmetry H2 fixing a particular point on the Coxeter plane is determined.

Character groups of dihedral and generalized quaternion groups

Finite abelian group duality appears in the discrete Fourier transform, or as the finite fragment of Pontryagin duality. The dual or character group of an abelian group encodes the products of its (linear) irreducible characters. Now, recent developments in combinatorics enable the construction of character groups for finite dihedral and generalized quaternion groups, encoding the products of all the irreducible characters (linear and nonlinear) in purely multiplicative fashion. In particular, just as in the abelian case, each dihedral group may serve as its own character group. Furthermore, certain Adams operations on the characters are shown to correspond to powers in the character group of a dihedral group.

Extra high-Q resonances and extraordinary transparency in finite fragments of dielectric metasurfaces: Prospects for 5G applications

We investigate the effects of fragmenting metasurfaces (MSs), composed of dielectric disks, on their electromagnetic responses and show that the presence of four abrupt boundaries between finite size structures and free space leads to the formation of new resonance modes. In addition to the characteristic for infinite metasurfaces modes with identical dipolar resonances formed in all unit cells, fragmented metasurfaces can exhibit out-of-phase electric and magnetic responses in neighboring “meta-atoms.” While in-phase responses correspond to field patterns representative for even resonance modes, out-of-phase responses produce a variety of patterns typical for odd resonance modes. These modes are formed as the result of partial reflections of surface waves from boundaries between MS fragments and free space, and their respective responses demonstrate extremely high intensities and Q-factors. Enabled by new responses, a significantly localized wave/matter interaction can be used for enhancing the performance of sensors and absorbers of 5G systems. In addition, we report the detection of extraordinary narrow-band transmission at electric and magnetic dipolar resonances in fragmented MSs that can be used to locally enhance mm-wave signals for 5G communications. As a proof of concept, transmission through a 5 × 5 MS fragment has been experimentally confirmed in the X-band of microwave spectrum.

UNUSUAL TYPES OF LAYERED ORGANIC CRYSTAL HYDRATES

In molecular crystalline hydrates with a high content of crystallization water infinite H2O...OH2 nets or finite fragments of such nets are formed. As a rule, these nets contain 5- and 6-membered cycles (H2O)n. Brand new topological types of layered organic crystal hydrates among the structures included in the Cambridge Structural Database in 2009–2019 were found and investigated. The discovered nets were deposited to the Topological Types Database. Topological characteristics of new nets are described, in particular, the maximum possible symmetry, information indices, vertex, edge and face transitivity of the nets

Breather arrest in a chain of damped oscillators with Hertzian contact

Breather propagation in a damped oscillatory chain with Hertzian nearest-neighbour coupling is investigated. The breather propagation exhibits an unusual two-stage pattern. The first stage is characterized by power-law decay of the breather amplitude. This stage extends over finite number of the chain sites. Drastic drop of the breather amplitude towards the end of this finite fragment is referred to as breather arrest. At the second stage, the breather exhibits very small amplitudes with hyper-exponential decay. Numeric results are rationalized by considering a simplified model of two damped linear oscillators coupled by Hertzian contact forces. Initial excitation of one of these oscillators results in a finite number of beating cycles in the system. This simplified model reliably predicts main features of the breather arrest. More general coupling potentials and effect of pre-compression on the breather propagation are also discussed.

Generalization of numerical quasiconformal mapping methods for geological problems

A method for identifying parameters of the conductivity coefficient of objects is generalized for the case of reconstructing an image of a part of a soil massif from the tomography data of the applied quasipotentials. In this case, without diminishing the generality, the reconstruction of the image is carried out in a fragment of a rectangular medium with local bursts of homogeneity present in it. The general idea of the corresponding algorithm consists in the sequential iterative solution of problems on quasiconformal mappings and identification of the parameters of the conductivity coefficient, with an insufficient amount of data on the values of the flow functions on the “inaccessible” part of the boundary. The image was reconstructed according to the data obtained using a full-range gradient array. The developed approach, in comparison with the existing ones, has a number of advantages that make it possible to increase the accuracy of identification of the conductivity coefficient. Namely, it provides an increase, in a qualitative sense, in the amount of input data, allows avoiding the use of Dirac delta functions when modeling areas of application of potentials and sufficiently flexibly take into account the mathematical aspects of the implementation of a quasiconformal mapping of a finite fragment of a half-plane onto a parametric polygon (domain of a complex quasipotential). The solution of the corresponding problem, in particular, occurs not in a single (fixed) investigated fragment of a rectangular soil massif, but in a number of smaller subdomains of the same shape, in the proposed optimal sequence. This saves machine time significantly. The prospects for further practical implementation of the proposed method follow from its ability to give an approximate result with relatively low costs (financial, time)

Programming of the Average Windward Area of Finite Element Fragments Based on MCSPS

In order to obtain the average windward area of the natural fragments in finite element method, a simulation model of the average windward area is established based on the Monte Carlo Subdivision Projection Method. The projection boundary of the fragments is obtained. Based on the cross multiplication, the simulation program of the windward area of the FE natural fragment is compiled. According to the concave and convex polygon vertices of the different quadrants, the average windward area of the finite element fragments is solved. The results show that the average windward area simulation program based on cross multiplication is applicable to the area of concave and convex polygons; the results of different quadrants of the same polygon are exactly the same; the program is applicable to the average windward area of simulation fragments with arbitrary irregular shape.

Generalized Dual-Root Lattice Transforms of Affine Weyl Groups

Discrete transforms of Weyl orbit functions on finite fragments of shifted dual root lattices are established. The congruence classes of the dual weight lattices intersected with the fundamental domains of the affine Weyl groups constitute the point sets of the transforms. The shifted weight lattices intersected with the fundamental domains of the extended dual affine Weyl groups form the sets of labels of Weyl orbit functions. The coinciding cardinality of the point and label sets and corresponding discrete orthogonality relations of Weyl orbit functions are demonstrated. The explicit counting formulas for the numbers of elements contained in the point and label sets are calculated. The forward and backward discrete Fourier-Weyl transforms, together with the associated interpolation and Plancherel formulas, are presented. The unitary transform matrices of the discrete transforms are exemplified for the case A 2 .

Control of Timed Discrete Event Systems with Ticked Linear Temporal Logic Constraints

This paper presents a novel method of synthesizing a fragment of a timed discrete event system(TDES),introducing a novel linear temporal logic(LTL), called ticked LTL$_f$. The ticked LTL$_f$ is given as an extension to LTL$_f$, where the semantics is defined over a finite execution fragment. Differently from the standard LTL$_f$, the formula is defined as a variant of metric temporal logic formula, where the temporal properties are described by counting the number of tick in the fragment of the TDES. Moreover, we provide a scheme that encodes the problem into a suitable one that can be solved by an integer linear programming (ILP). The effectiveness of the proposed approach is illustrated through a numerical example of a path planning.

Generalization of the mode-matching technique to the problems of scattering by semi-infinite slow-wave structures

Subject and purpose. The scattering matrix of a semi-infinite slow-wave structure formed by grooves in a rectangular waveguide is investigated. The purpose was to develop a method for calculating a semi-infinite periodic structure. Methods and methodology. A generalization of the mode-matching technique to semi-infinite periodic structures is built. The fields of the periodic part of the structure are expanded in series of the eigenmodes of the periodic structure, taking into account the condition at infinity, which makes it possible to obtain a linear matrix equation for finding the scattering matrix. Only the propagating modes of the periodic structure were considered. To make these expansions reliable the fields were matched at a period somewhat distant from the junction of the regular waveguide with the periodic one. Results. Matrix equations for determining the blocks of the scattering matrix of a semi-infinite structure are obtained. A number of investigations are carried out to check the reliability of the equations obtained. These include test of convergence, reciprocity, energy balance, and conservation of the scattering matrix while adding one period to a semi-infinite structure. The main confirmation was obtained by comparing the scattering matrix of a finite fragment of the slow-wave structure, obtained in two ways: through the scattering matrices of semi-infinite slow-wave structure and through a cascade assembly of the scattering matrices of the waveguide elements that make up the structure. Conclusions. An algorithm for calculating the scattering matrix of a semi-infinite structure is obtained. It can be used to build a rigorous hot model of vacuum electronics devices using slow-wave structures.

Method for Measuring the Intelligibility of Speech Signals in the Kullback–Leibler Information Metric

We consider the problem of determination of the intelligibility of speech of a speaker according to a finite fragment of the speech signal. It is shown that the main difficulties in the solution of this problem are connected with the necessity of analysis of small samples. To overcome the problem of small samples, we proposed a new high-speed method for measuring the intelligibility of speech signals on the sonic level of its perception. The proposed method is based on the information indicator of speech intelligibility in the Kullback-Leibler metric. We consider an example of practical realization of the new method with the use of a self-regression model of minimum sound units from the speech flow of a speaker. The characteristics of efficiency of the new method are analyzed. It is shown that, under certain conditions, the application of the information indicator enables us to realize the general systems principle of guaranteed result. On the basis of the software developed by the authors, we designed and performed full-scale experiments and established quantitative estimates for the speed of this method. It is shown that, with the help of this method, quite accurate and reliable estimates of the information indicator are obtained for short (2–3 min) segments of speech signals. The accumulated results and the conclusions made on their basis are intended for applications in the development of new systems and improvement of the existing systems of automatic speech processing and recognition intended for the operation in the real-time mode.

Decomposition matrices for the square lattices of the Lie groups SU(2)times SU(2)

A method for the decomposition of data functions sampled on a finite fragment of rectangular lattice is described. The symmetry of a square lattice in a 2-dimensional real Euclidean space is either given by the semisimple Lie group SU(2)times SU(2) or equivalently by the Lie algebra A_1times A_1, or by the simple Lie group O(5) or its Lie algebra called C_2 or equivalently B_2. In this paper we consider the first of these possibilities which is applied to data which is given in 2 orthogonal directions—hence the method is a concatenation of two 1-dimensional cases. The asymmetry we underline here is a different density of discrete data points in the two orthogonal directions which cannot be studied with the simple Lie group symmetry.

Research of evolution of the stress strain and definition of the estimated life-time of massive structure elements using of the universal finite element

Mathematical modeling of the continual fracture processes under long creep conditions on the basis of FEM is a rather complex problem. The efficiency of solving of this problem depends on the completeness of the finite element library and the algorithms for solving systems of nonlinear equations, as well as on the software organization. The main principles of the moment sheme of finite elements (MSFE) is the base for procedure of obtaining of finite-element solving relationships. In contrast to the generally accepted approaches the use of MSFE provides an independent representation of deformations in the form of Maclaurin series in addition to the choose of the law of displacements distribution. At the base of the algorithm for solving a system of nonlinear equations, the method of integration over the load parameter is adopted. It is assumed to reduce an integration step consecutively to obtain reliable results. To optimize discrete FEM models, an approach based on the initial fragmentation of the computational model was used. The accuracy of solving of a system of nonlinear equations at each step of the load parameter is determined by comparing the sum of the squares of the nodal reactions and the sum of the squares of the nodal values of the external loads. The equations of termoviscolastoplastic deformation taking into account the damage of materials are taken as initial relations. The principle of using of quasiregular fragmentation which involves constructing a general irregular finite element model based on regular finite element fragments is basis of the procedure of constructing the finite element model of objects under consideration. This make it possible to optimize substantially the total number of unknowns. When calculating of a new objects, the convergence of the results is justified by a sequential increase of the parameters of the mesh model, a decrease of integration step value due to an increase of their number within a given range of loads, and an increase of the accuracy of solving of nonlinear equations system at each step. In order to justify the reliability of the results, obtained on the basis of the universal finite element, the parameters of the stress-strain state and the damage parameter ω were compared with data calculated on the basis of finite elements of a general type with numerical integration and elements with integration in a closed form.

Decomposition matrices for the special case of data on the triangular lattice of G(2)

A method for the decomposition of data functions sampled on a finite fragment of triangular lattice is described for the cases of lattices of any density corresponding to the simple Lie group G ( 2 ) . Its main advantage is the fact that the decomposition matrix needs to be calculated only once for arbitrary sets of data sampled on the same set of discrete points. The decomposition matrix applies to lattice of any density that carries data.

Addressing infinite-horizon optimization in MPC via Q-learning

Model predictive control (MPC) is the standard approach to infinite-horizon optimal control which usually optimizes a finite initial fragment of the cost function so as to make the problem computationally tractable. Globally optimal controllers are usually found by Dynamic Programming (DP). The computations involved in DP are notoriously hard to perform, especially in online control. Therefore, different approximation schemes of DP, the so-called “critics”, were suggested for infinite-horizon cost functions. This work proposes to incorporate such a critic into dual-mode MPC as a particular means of addressing infinite-horizon optimal control. The proposed critic is based on Q-learning and is used for online approximation of the infinite-horizon cost. Stability of the new approach is analyzed and certain sufficient stabilizing constraints on the critic are derived. A case study demonstrates the applicability.