Unique Decomposition Research Articles

Retrieving the GBT modal decomposition from large displacement shell finite element results

This paper proposes an efficient procedure to post-process non-linear shell finite element analysis results, in order to recover the unique modal decomposition features of Generalised Beam Theory (GBT). This procedure extends, to the large displacement range, a previous one developed for first-order elastoplastic, bifurcation and vibration analyses of thin-walled members (Manta et al., 2021). This means that the structural insight typically obtained through GBT analyses can be quite straightforwardly recovered from shell finite element collapse analysis results. The proposed procedure retrieves modal strains rather than modal displacements, since the GBT kinematic description is not suited to describe cross-section finite rotations. To show the capabilities and potential of the proposed procedure, two validation examples, in which a comparison with analytical solutions is made, and two application examples, involving large displacements and plasticity, are presented and discussed.

Projections of modular forms on Eisenstein series and its application to Siegel’s formula

Let \(k \ge 2\) and N be positive integers and let \(\chi \) be a Dirichlet character modulo N. Let f(z) be a modular form in \(M_k(\Gamma _0(N),\chi )\). Then we have a unique decomposition \(f(z)=E_f(z)+S_f(z)\), where \(E_f(z) \in E_k(\Gamma _0(N),\chi )\) and \(S_f(z) \in S_k(\Gamma _0(N),\chi )\). In this paper, we give an explicit formula for \(E_f(z)\) in terms of Eisenstein series whose coefficients are sum of divisors function. Then we apply our result to certain families of eta quotients and to representations of positive integers by 2k–ary positive definite quadratic forms in order to give an alternative version of Siegel’s formula for the weighted average number of representations of an integer by quadratic forms in the same genus. Our formula for the latter is in terms of sum of divisors function and does not involve computation of local densities.

Generalized persistence algorithm for decomposing multiparameter persistence modules

The classical persistence algorithm computes the unique decomposition of a persistence module implicitly given by an input simplicial filtration. Based on matrix reduction, this algorithm is a cornerstone of the emergent area of topological data analysis. Its input is a simplicial filtration defined over the integers $${\mathbb {Z}}$$ giving rise to a 1-parameter persistence module. It has been recognized that multiparameter version of persistence modules given by simplicial filtrations over d-dimensional integer grids $${\mathbb {Z}}^d$$ is equally or perhaps more important in data science applications. However, in the multiparameter setting, one of the main challenges is that topological summaries based on algebraic structure such as decompositions and bottleneck distances cannot be as efficiently computed as in the 1-parameter case because there is no known extension of the persistence algorithm to multiparameter persistence modules. We present an efficient algorithm to compute the unique decomposition of a finitely presented persistence module M defined over the multiparameter $${\mathbb {Z}}^d$$ . The algorithm first assumes that the module is presented with a set of N generators and relations that are distinctly graded. Based on a generalized matrix reduction technique it runs in $$O(N^{2\omega +1})$$ time where $$\omega <2.373$$ is the exponent of matrix multiplication. This is much better than the well known algorithm called Meataxe which runs in $${\tilde{O}}(N^{6(d+1)})$$ time on such an input. In practice, persistence modules are usually induced by simplicial filtrations. With such an input consisting of n simplices, our algorithm runs in $$O(n^{(d-1)(2\omega + 1)})$$ time for $$d\ge 2$$ . For the special case of zero dimensional homology, it runs in time $$O(n^{2\omega +1})$$ .

Simulation of flow in deformable fractures using a quasi-Newton based partitioned coupling approach

We introduce a partitioned coupling approach for iterative coupling of flow processes in deformable fractures embedded in a poro-elastic medium that is enhanced by interface quasi-Newton (IQN) methods. In this scope, a unique computational decomposition into a fracture flow and a poro-elastic domain is developed, where communication and numerical coupling of the individual solvers are realized by consulting the open-source library preCICE. The underlying physical problem is introduced by a brief derivation of the governing equations and interface conditions of fracture flow and poro-elastic domain followed by a detailed discussion of the partitioned coupling scheme. We evaluate the proposed implementation and undertake a convergence study to compare a classical interface quasi-Newton inverse least-squares (IQN-ILS) with the more advanced interface quasi-Newton inverse multi-vector Jacobian (IQN-IMVJ) method. These coupling approaches are verified for an academic test case before the generality of the proposed strategy is demonstrated by simulations of two complex fracture networks. In contrast to the development of specific solvers, we promote the simplicity and computational efficiency of the proposed partitioned coupling approach using preCICE and FEniCS for parallel computations of hydro-mechanical processes in complex, three-dimensional fracture networks.

Linking the Spectra of Decomposing Litter to Ecosystem Processes: Tandem Close-Range Hyperspectral Imagery and Decomposition Metrics

Efforts to monitor terrestrial decomposition dynamics at broad spatial scales are hampered by the lack of a cost-effective and scalable means to track the decomposition process. Recent advances in remote sensing have enabled the simulation of litter spectra throughout decomposition for grasses in general, yet unique decomposition pathways are hypothesized to create subtly different litter spectral signatures with unique ecosystem functional significance. The objectives of this study were to improve spectra–decomposition linkages and thereby enable the more comprehensive monitoring of ecosystem processes such as nutrient and carbon cycles. Using close-range hyperspectral imaging, litter spectra and multiple decomposition metrics were concurrently monitored in four classes of naturally decayed litter under four decomposition treatments. The first principal component accounted for approximately 94% of spectral variation in the close-range imagery and was attributed to the progression of decomposition. Decomposition-induced spectral changes were moderately correlated with the leaf carbon to nitrogen ratio (R2 = 0.52) and sodium hydroxide extractables (R2 = 0.45) but had no correlation with carbon dioxide flux. Temperature and humidity strongly influenced the decomposition process but did not influence spectral variability or the patterns of surface decomposition. The outcome of the study is that litter spectra are linked to important metrics of decomposition and thus remote sensing could be utilized to assess decomposition dynamics and the implications for nutrient recycling at broad spatial scales. A secondary study outcome is the need to resolve methodological challenges related to inducing unique decomposition pathways in a lab environment. Improving decomposition treatments that mimic real-world conditions of temperature, humidity, insolation, and the decomposer community will enable an improved understanding of the impacts of climatic change, which are expected to strongly affect microbially mediated decomposition.

Spectrally Resolved Raman Lidar to Measure Backscatter Spectra of Atmospheric Three-Phase Water and Fluorescent Aerosols Simultaneously: Instrument, Methodology, and Preliminary Results

This work presents a spectrally resolved Raman lidar (SRRL) for simultaneous measurement of volume backscattering coefficient spectra (backscatter spectra for short) of atmospheric three-phase water and fluorescent aerosols. The SRRL emits 354.8-nm laser light and records both N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> Raman echoes around 386.7 nm and spectral signals in a specially modified spectral range of ~393–424 nm. By defining normalized spectra, a unique spectra decomposition approach is developed for successive retrieval of normalized spectra components of fluorescent aerosols, water vapor, ice water, and liquid water. Furthermore, the backscatter spectra of each component are obtained by referencing the N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> Raman signals. Three typical measurement cases are provided. For the clear-day case, the lidar-measured normalized water vapor Raman spectra are found to be nearly invariant in shape and can serve as background spectra reference for decomposition of mixed-phase water Raman spectra. Besides, fluorescence backscatter intensities are usually weak enough to be neglected in clear areas. For the fluorescence case, the fluorescence backscatter intensities become much stronger to prevent accurate measurements of water vapor. For the mixed-phase water virga case, the decomposed backscatter spectra of condensed ice and liquid water indicate the coexistence of ice water and less amount of liquid water in the falling water virga. In conclusion, this kind of SRRL is believed to have provided the potential for simultaneous and accurate profiling of atmospheric water vapor and cloud liquid/ice water and opened up new perspectives for studies of cloud–aerosol interaction.

Unique surface structure resulting in the excellent long-term thermal stability of Fe4Sb12-based filled skutterudites

The evolutions of the phase composition, microstructure, and thermoelectric properties of BaFe4Sb12 materials at 773 K in vacuum were investigated to evaluate their long-term thermal stabilities. It was observed that the interior of the BaFe4Sb12 exhibited excellent thermal stability, while the surface decomposed into FeSb2, Sb, and Ba5Sb3. However, the decomposition rate sharply declined with increasing annealing time, and the thicknesses of the decomposition layer was approximately 49 μm after annealing for 30 days. Thermoelectric performances negligibly changed during the annealing process, and the dimensionless figure of merit remained in the range of 0.61 ± 0.02 at 800 K. The unique decomposition layer, wherein Ba5Sb3 compounds enriched in the outermost layer and along the FeSb2 grain boundaries, served as a dense protective cover to effectively retard the Sb sublimation, resulting in excellent long-term thermal stability. This work provides a plausible explanation for the long-term thermal stability of Fe4Sb12-based filled skutterudites.

Pure-jump semimartingales

A new integral with respect to an integer-valued random measure is introduced. In contrast to the finite variation integral ubiquitous in semimartingale theory (Jacod and Shiryaev, 2003, II.1.5), the new integral is closed under stochastic integration, composition, and smooth transformations. The new integral gives rise to a previously unstudied class of pure-jump processes: the sigma-locally finite variation pure-jump processes. As an application, it is shown that every semimartingale $X$ has a unique decomposition $$X = X_0 + X^{\mathrm{qc}}+X^{\mathrm{dp}},$$ where $X^{\mathrm{qc}}$ is quasi-left-continuous and $X^{\mathrm{dp}}$ is a sigma-locally finite variation pure-jump process that jumps only at predictable times, both starting at zero. The decomposition mirrors the classical result for local martingales (Yoeurp, 1976, Theoreme~1.4) and gives a rigorous meaning to the notions of continuous-time and discrete-time components of a semimartingale. Against this backdrop, the paper investigates a wider class of processes that are equal to the sum of their jumps in the semimartingale topology and constructs a taxonomic hierarchy of pure-jump semimartingales.

Efficiency decomposition in a three-stage network structure: Cooperative DEA, Nash bargaining game models and conic relaxations

In this paper, for evaluating the efficiency in a three-stage DEA structure we use the additive and the multiplicative cooperative models that comply with the cooperation paradigm in the organizations, where for improving efficiency of system, stages cooperate together. Since the overall efficiency from the cooperative models may not be unique and consequently the stages’ efficiencies, then we combine them with the Nash bargaining game approach that besides maximizing efficiency scores for stages and the whole system, provides a unique and fair efficiency decomposition. Second order programming relaxation of the proposed nonlinear models are given in contrast to the parametric linear models in the literature. Finally, the effectiveness of the proposed models are illustrated with two numerical examples.

Normal orthogonality spaces

An orthogonality space is a set X together with a symmetric and irreflexive binary relation ⊥, called the orthogonality relation. A block partition of X is a partition of a maximal set of mutually orthogonal elements of X, and a decomposition of X is a collection of subsets of X each of which is the orthogonal complement of the union of the others. (X,⊥) is called normal if any block partition gives rise to a unique decomposition of the space. The set of one-dimensional subspaces of a Hilbert space equipped with the usual orthogonality relation provides the motivating example. Together with the maps that are, in a natural sense, compatible with the formation of decompositions from block partitions, the normal orthogonality spaces form a category, denoted by NOS. The objective of the present paper is to characterise both the objects and the morphisms of NOS from various perspectives as well as to compile basic categorical properties of NOS.

Tensor products of coherent configurations

A Cartesian decomposition of a coherent configuration \({\cal X}\) is defined as a special set of its parabolics that form a Cartesian decomposition of the underlying set. It turns out that every tensor decomposition of \({\cal X}\) comes from a certain Cartesian decomposition. It is proved that if the coherent configuration \({\cal X}\) is thick, then there is a unique maximal Cartesian decomposition of \({\cal X}\), i.e., there is exactly one internal tensor decomposition of \({\cal X}\) into indecomposable components. In particular, this implies an analog of the Krull-Schmidt theorem for the thick coherent configurations. A polynomial-time algorithm for finding the maximal Cartesian decomposition of a thick coherent configuration is constructed.

Graphical interpretation of non-negative factorization expecting bio-Raman research

Non-negative matrix factorization (NMF) has been frequently used in research on live cells, biomolecules, and tissues (bio-Raman research) to disentangle the complicated and large sized data. A stagnation is that NMF does not provide unique decomposition, depending on initial settings; that is, NMF returns non-negative spectral components close to the truths, but solely giving several possibilities. In this research, we visualized possible ranges of NMF in binary component system. The mechanism of NMF became more clarified and opened new viewpoints.

Retrieving GBT mode amplitudes from shell finite element and finite strip results in first-order elastoplastic, bifurcation and vibration analyses

This paper presents a general post-processing procedure that enables retrieving GBT deformation mode amplitudes directly from shell finite element or finite strip results with a small computational cost. The procedure extends that for proposed in Cai (2019), in the context of bifurcation analyses, to all deformation mode families (conventional, shear and transverse extension), several analysis types (first-order elastic/elastoplastic and vibration) and problems with complex geometry (e.g., tapered or curved parts), which are difficult to analyse or cannot be analysed with GBT. Therefore, the unique GBT modal decomposition features, making it possible to acquire in-depth insight into the underlying mechanics, can be used even in complex problems. In order to demonstrate the accuracy of the proposed procedure, several validation examples are presented, involving problems for which “pure” GBT analyses can be performed. Finally, a set of application examples are provided, to show the capabilities and potential of this new approach.

Enabling Lithium Metal Anode in Nonflammable Phosphate Electrolyte with Electrochemically Induced Chemical Reactions.

Lithium metal anode holds great promises for next-generation battery technologies but is notoriously difficult to work with. The key to solving this challenge is believed to lie in the ability of forming stable solid-electrolyte interphase (SEI) layers. To further address potential safety issues, it is critical to achieve this goal in nonflammable electrolytes. Building upon previous successes in forming stable SEI in conventional carbonate-based electrolytes, here we report that reversible Li stripping/plating could be realized in triethyl phosphate (TEP), a known flame retardant. The critical enabling factor of our approach was the introduction of oxygen, which upon electrochemical reduction induces the initial decomposition of TEP and produces Li3 PO4 and poly-phosphates. Importantly, the reaction was self-limiting, and the resulting material regulated Li plating by limiting dendrite formation. In effect, we obtained a functional SEI on Li metal in a nonflammable electrolyte. When tested in a symmetric Li∥Li cell, more than 300 cycles of stripping/plating were measured at a current density of 0.5 mA cm-2 . Prototypical Li-O2 and Li-ion batteries were also fabricated and tested to further support the effectiveness of this strategy. The mechanism by which the SEI forms was studied by density functional theory (DFT), and the predictions were corroborated by the successful detection of the intermediates and products.

The two-loop remainder function for eight and nine particles

Two-loop MHV amplitudes in planar mathcal{N} = 4 supersymmetric Yang Mills theory are known to exhibit many intriguing forms of cluster-algebraic structure. We leverage this structure to upgrade the symbols of the eight- and nine-particle amplitudes to complete analytic functions. This is done by systematically projecting onto the components of these amplitudes that take different functional forms, and matching each component to an ansatz of multiple polylogarithms with negative cluster-coordinate arguments. The remaining additive constant can be determined analytically by comparing the collinear limit of each amplitude to known lower-multiplicity results. We also observe that the nonclassical part of each of these amplitudes admits a unique decomposition in terms of a specific A3 cluster polylogarithm, and explore the numerical behavior of the remainder function along lines in the positive region.

A comprehensive kinetic study on the speciation from propylene and propyne pyrolysis in a single-pulse shock tube

This work is centered on the speciation from propylene and propyne pyrolysis by means of shock tube experiments and detailed kinetic modeling. A wealth of intermediates and products, covering small acyclic hydrocarbons up to four-ring aromatics, are probed from the C3 fuels pyrolysis at a nominal pressure of 20 bar over 1050–1650 K. With updates in reactions involving C3 species, our on-going polycyclic aromatic hydrocarbon (PAH) formation kinetic model can well predict the measurements obtained in the current work as well as relevant literature data. Propyne exhibits a unique two-stage decomposition profile, as the characteristic isomerization to allene dominates in its consumption at moderate temperatures below 1300 K. Overall, propylene pyrolysis results in more diverse small hydrocarbons, but much lower contents of aromatics, in comparison to propyne pyrolysis. In both studied cases, the formation of benzene is dependent upon the propargyl recombination, and since propyne decomposition induces a more rapid and more plentiful propargyl production, benzene mole fractions are much higher in propyne pyrolysis. In both cases, naphthalene is observed as the most abundant PAH species, followed by acenaphthalene. Modeling analyses indicate that similar reaction pathways are responsible for the PAH formation in propylene and propyne pyrolysis. Indene is formed from the interactions between benzene/phenyl and C3 species, through its non-PAH isomers as intermediates. The subsequent reactions of indenyl radical with methyl and propargyl are essential pathways leading to naphthalene and acenaphthalene, respectively. Naphthyl radical further participates in the formation of different larger PAHs. The methylene-substituted cyclopenta-ring species are deemed as important precursors of their aromatic isomers, as is noted from the fulvene-to-benzene, benzofulvene-to-naphthalene and 9-methylene-fluorene-to-phenanthrene conversions.

A novel method for determining the feasible integral self-stress states for tensegrity structures

Abstract The form-finding analysis is a crucial step for determining the stable self-equilibrated states for tensegrity structures, in the absence of external loads. This form-finding problem leads to the evaluation of both the self-stress in the elements and the shape of the tensegrity structure. This paper presents a novel method for determining feasible integral self-stress states for tensegrity structures, that is self-equilibrated states consistent with the unilateral behaviour of the elements, struts in compression and cables in tension, and with the symmetry properties of the structure. In particular, once defined the connectivity between the elements and the nodal coordinates, the feasible self-stress states are determined by suitably investigating the Distributed Static Indeterminacy (DSI). The proposed method allows for obtaining feasible integral self-stress solutions by a unique Singular Value Decomposition (SVD) of the equilibrium matrix, whereas other approaches in the literature require two SVD. Moreover, the proposed approach allows for effectively determining the Force Denstiy matrix, whose properties are strictly related to the super-stability of the tensegrity structures. Three tensegrity structures were studied in order to assess and discuss the efficiency and accuracy of the proposed innovative method.

Simplex-Structured Matrix Factorization: Sparsity-Based Identifiability and Provably Correct Algorithms

In this paper, we provide novel algorithms with identifiability guarantees for simplex-structured matrix factorization (SSMF), a generalization of nonnegative matrix factorization. Current state-of-the-art algorithms that provide identifiability results for SSMF rely on the sufficiently scattered condition (SSC) which requires the data points to be well spread within the convex hull of the basis vectors. The conditions under which our proposed algorithms recover the unique decomposition is in most cases much weaker than the SSC. We only require to have $d$ points on each facet of the convex hull of the basis vectors whose dimension is $d-1$. The key idea is based on extracting facets containing the largest number of points. We illustrate the effectiveness of our approach on synthetic data sets and hyperspectral images, showing that it outperforms state-of-the-art SSMF algorithms as it is able to handle higher noise levels, rank deficient matrices, outliers, and input data that highly violates the SSC.

Research on decomposition rate of fungi based on temperature and humidity model

Fungus is one of the decomposers in biosphere. Through its unique decomposition effect, it decomposes, converts and absorbs the organic matters in animal and plant remains of the humus layer. Fugus plays an essential role in not merely maintaining the carbon cycle but ensuring the ecosystem on earth under the environment of geochemical cycle, which is beneficial to the stability of the Earth’s environment and the sustainable development of biodiversity. Our team simulated the decomposition of fungi by establishing a mathematical model, aiming to study the following questions: How do fungi with different traits interact and decompose the litter layer in a given land environment; What effect will moisture and temperature have on the decomposition process of fungi in different environments; environmental change trends and kinetic significance; fungal competition in a specific environment; taking into account the growth rate, the decomposition rate of fungi is estimated by the model . A variety of methods are used in the process of model establishment and data analysis: ‘single variable control’ experiment, Python software data analysis, Matlab software data analysis, system dynamics analysis and error analyzing and processing. Strictly control the simulation experiment conditions, guarantee the scientificity and rationality of the experimental data, eliminate interference factors, reduce gross errors, and improve the accuracy of experimental data.

A study on strongly convex hyper S-subposets in hyper S-posets

Abstract In this paper, we study various strongly convex hyper S-subposets of hyper S-posets in detail. To begin with, we consider the decomposition of hyper S-posets. A unique decomposition theorem for hyper S-posets is given based on strongly convex indecomposable hyper S-subposets. Furthermore, we discuss the properties of minimal and maximal strongly convex hyper S-subposets of hyper S-posets. In the sequel, the concept of hyper C-subposets of a hyper S-poset is introduced, and several related properties are investigated. In particular, we discuss the relationship between greatest strongly convex hyper S-subposets and hyper C-subposets of hyper S-posets. Moreover, we introduce the concept of bases of a hyper S-poset and give out the sufficient and necessary conditions of the existence of the greatest hyper C-subposets of a hyper S-poset by the properties of bases.