Local Basis Research Articles

Dictionary-based online-adaptive structure-preserving model order reduction for parametric Hamiltonian systems

Classical model order reduction (MOR) for parametric problems may become computationally inefficient due to large sizes of the required projection bases, especially for problems with slowly decaying Kolmogorov n-widths. Additionally, Hamiltonian structure of dynamical systems may be available and should be preserved during the reduction. In the current presentation, we address these two aspects by proposing a corresponding dictionary-based, online-adaptive MOR approach. The method requires dictionaries for the state-variable, non-linearities, and discrete empirical interpolation (DEIM) points. During the online simulation, local basis extensions/simplifications are performed in an online-efficient way, i.e., the runtime complexity of basis modifications and online simulation of the reduced models do not depend on the full state dimension. Experiments on a linear wave equation and a non-linear Sine-Gordon example demonstrate the efficiency of the approach.

Numerical simulation of spatio-temporal spread of an infectious disease utilizing a collocation method based on local radial basis functions

Numerical simulation of spatio-temporal spread of an infectious disease utilizing a collocation method based on local radial basis functions

Time-periodic natural convection in a pentagonal house with pitched roof during one day

A numerical investigation of unsteady natural convective flow and heat transfer in a pentagonal house is performed. We set a sinusoidal periodic heat flux boundary condition for the pitched roof. Local radial basis function method and Fourier spectral method are adopted to solve the governing equations. The Rayleigh number varies from 103 to 105, the period of the roof heat flux ranges from 10 to 1,000, and the amplitude is set as 0.1, 0.3, and 0.5, respectively. It is found that all the control parameters significantly impact the fluid flow and heat transfer. The temperature and flow fields exhibit periodic behavior due to the sinusoidal heat source. The increasing Rayleigh number leads to a larger periodic average Nusselt number of the top and right walls and a smaller value of the bottom wall. Moreover, an obvious hysteresis phenomenon of heat transfer occurs especially for high Rayleigh number and large period.

System identification and monitoring of bridge structures

The research presented is part of the SPP100+ of the German Research Foundation. Subject of the research is the early detection of damage, especially on large bridge structures. For this purpose, investigations are carried out at the technical center of the I4S, in particular to take into account the environmental conditions (EOC) in the context of system identification of mechanical structures. The lifetime of the considered structures is divided into macro and micro time domains. In the micro time domain, state space models serve as a basis for damage localization. The parameters of the models are estimated based on output-only methods and H2/H∞ optimization. The damage localization is done by SP2E, the state projection estimation error method in conjunction with a machine learning method, for the categorization of the EOC. This paper presents the monitoring method in micro time domain of lifetime and first results of experimental investigation and vibration-based output-only measurements at the bridge Floßgrabenbrücke.

An Efficient Local Radial Basis Function Method for Image Segmentation Based on the Chan–Vese Model

An Efficient Local Radial Basis Function Method for Image Segmentation Based on the Chan–Vese Model

A LOCALIZED MESHLESS METHOD FOR TRANSIENT HEAT CONDUCTION WITH APPLICATIONS

The localized radial basis function (RBF) meshless approach is well suited for modeling transient heat conduction. The advantages of meshless methods, such as ease of discretization, are well known. However, there are still few examples of the method extended to three-dimensional (3D) transient heat conduction for geometries of practical engineering importance; in particular, with respect to graphics processing units (GPUs). In this study, we investigated the localized RBF meshless method in 3D transient heat conduction and explored its application for GPUs. Numerical examples are provided with an application to modeling chip cooling and friction welding.

Phase transitions and spectral shifts: a quantum mechanical exploration of vibrational frequency in magnesium ferrite.

Spinel ferrites represent an integral subset of magnetic materials, with their inherent properties largely influenced by cation occupancy and spin interaction. In this study, we present an in-depth theoretical exploration of the phase transition landscape of pure magnesium-ferrite, deploying hybrid functionals and a local Gaussian basis set to scrutinize the relaxed lattice structure, relative energy, magnetic properties, electronic characteristics, and vibrational frequencies. Our investigation reveals that the ground state of magnesium-ferrite is an open-shell system with an inverse structure. This is characterized by the complete occupancy of octahedral sites by magnesium atoms, with Iron atoms dispersed between both tetrahedral and octahedral sites. We found a relative energy difference of 0.41 eV between the antiferromagnetic ground configuration and the ferro arrangement within the inverse structure. Furthermore, our research also delved into the impact of spin rearrangement and inversion (X = 0.0, 0.5 and 1) on Raman and infrared spectra. Notably, the lattice distortion from the cubic form, apparent in the optimized structure, resonates in the IR and Raman spectra, resulting in significant splitting. The frequencies calculated in this study align well with experimental values, suggesting that the literature's current assignments warrant reevaluation in light of this new data. The results presented herein can be instrumental in detecting the phase of Mg ferrites from experimental spectra, thereby paving the way for a more profound comprehension of their properties and possible uses.

Hydraulic cylinder rod part surface quality improvement on the local thermal effect basis

In modern mechanical engineering, one of the urgent tasks is to improve the quality of manufacturing of surfaces of contact pairs of hydraulic cylinders. This task is connected, first of all, with the grinding operation, which leads to the formation of burns, microcracks, and scarring. The presence of defects on the surface leads to the formation of a poor-quality protective chrome layer. Destruction of the protective layer during operation breaks the sealing ability of the sealing rings. For this reason, abrasive microparticles enter the contact zone, forming adhesive wear on the surfaces. To increase the performance characteristics of hydraulic cylinders, it is necessary to comply with the quality requirements in the technological process. So, for the part “rod” surface roughness should be Ra = 0.63 μm. It is possible to achieve a given surface quality by replacing the grinding operation with mechanical processing with local thermal influence.

The true twin classes-based investigation for connected local dimensions of connected graphs

<abstract><p>Let $ G $ be a connected graph of order $ n $. The representation of a vertex $ v $ of $ G $ with respect to an ordered set $ W = \{w_1, w_2, ..., w_k\} $ is the $ k $-vector $ r(v|W) = (d(v, w_1), d(v, w_2), ..., d(v, w_k)) $, where $ d(v, w_i) $ represents the distance between vertices $ v $ and $ w_i $ for $ 1\leq i\leq k $. An ordered set $ W $ is called a connected local resolving set of $ G $ if distinct adjacent vertices have distinct representations with respect to $ W $, and the subgraph $ \langle W\rangle $ induced by $ W $ is connected. A connected local resolving set of $ G $ of minimum cardinality is a connected local basis of $ G $, and this cardinality is the connected local dimension $ \mathop{\text{cld}}(G) $ of $ G $. Two vertices $ u $ and $ v $ of $ G $ are true twins if $ N[u] = N[v] $. In this paper, we establish a fundamental property of a connected local basis of a connected graph $ G $. We analyze the connected local dimension of a connected graph without a singleton true twin class and explore cases involving singleton true twin classes. Our investigation reveals that a graph of order $ n $ contains at most two non-singleton true twin classes when $ \mathop{\text{cld}}(G) = n-2 $. Essentially, our work contributes to the characterization of graphs with a connected local dimension of $ n-2 $.</p></abstract>

Intranipple injection with methylene blue for tracing axillary sentinel lymph nodes in rats: A preliminary feasibility study

Background and purpose: Investigate the feasibility of intranipple injection (INN) of methylene blue dye (MB) for tracing the axillary sentinel lymph node (SLN) in rats, to provide different injection methods for finding SLN injection tracers and offer an experimental basis for specific localization of SLN. Methods: Eleven Sprague-Dawley female rats with body masses of 150-400g. Ten rats were randomly selected to use the third pair of mammary glands as the tracer injection site, and the left side was injected with MB (0.05 mL, 1% concentration) by intracutaneous injection of areola (IAA), while the right side was injected with MB(0.05 mL, 1% concentration) by INN. After 5 minutes, the rats were dislocated and dissected, and the blue-stained SLNs were found and recorded, The effectiveness evaluation was based on the number and rate of detection of SLNs as indicators, and the differences between the indicators of the two injection methods of IAA and INN were compared and analyzed. The safety evaluation was based on whether the nipple showed blood flow disorders and necrosis after MB injection by INN in the remaining 1 rat as the criteria. The data were stored and analyzed using Microsoft Excel and SPSS 25.0 statistical software. Νon-normally distributed measurement data were expressed as M (Q1, Q3) and compared by rank sum test, and count data were expressed as cases or percentages and compared by 2 test. p < 0.05 was considered a statistically significant difference. Results: (i)100% (10/10) detection rate of SLNs by applying MB to both INN and IAA modalities;(ii) median number of SLNs detection was 2.0 (1.0,2.0) vs. 1.5 (1.0,2.0) for INN and IAA, respectively (P=0.66), and the difference was not statistically significant;(iii) No nipple necrosis was observed for 4 consecutive days after INN with MB. Conclusion: Tracer detection of SLNs by INN injection in rats is feasible, and the detection rate of SLNs by INN is the same as that of IAA; there is no significant difference in the median number of detected SLNs between the two injection methods. No nipple necrosis was observed after INN with MB.

Spatiotemporal change in vegetation cover in the Yellow River Basin between 2000 and 2022 and driving forces analysis

In this paper, we investigate the features of spatiotemporal change in fractional vegetation cover (FVC) throughout the Yellow River Basin between 2000 and 2022 and identify the driving factors behind the change using the MODIS normalized difference vegetation index (NDVI) as a data source. On that basis, our research involves trend analysis and the center migration model to examine the correlation between vegetation cover changes and various factors, such as climates, topographies, soils, and human activities. In this way, we aim to uncover how such correlation contributed to the reduction in suspended sediment concentration (SSC) in surface runoff. Results suggest that (1) the FVC of the Yellow River Basin has been trending upward over the past 23 years, and vegetation growth has been remarkably improved; (2) the center of medium-high and denser vegetation cover has progressively migrated from the upper reaches of the Yellow River down to its middle-lower segments; (3) soil erosion control measures are critical to improve vegetation cover, given the great impact of the shifting natural elements on vegetation cover changes on a local basis; (4) an improvement in vegetation cover leads to considerable positive change in the runoff and SSC of the Yellow River mainstem. This study has yielded noteworthy contributions in correctly understanding the current vegetation changes and related factors in the Yellow River Basin. Furthermore, it has laid the groundwork for further research in improving the accuracy of basic data and deepening the correlation between factors.

Hyperparameter Optimization of an hp-Greedy Reduced Basis for Gravitational Wave Surrogates

In a previous work, we introduced, in the context of gravitational wave science, an initial study on an automated domain-decomposition approach for a reduced basis through hp-greedy refinement. The approach constructs local reduced bases of lower dimensionality than global ones, with the same or higher accuracy. These “light” local bases should imply both faster evaluations when predicting new waveforms and faster data analysis, particularly faster statistical inference (the forward and inverse problems, respectively). In this approach, however, we have previously found important dependence on several hyperparameters, which do not appear in a global reduced basis. This naturally leads to the problem of hyperparameter optimization (HPO), which is the subject of this paper. Here, we compare the efficiency of the Bayesian approach against grid and random searches, which are two order of magnitude slower. Then, we tackle the problem of HPO through Bayesian optimization.We find that, for the cases studied here of gravitational waves from the collision of two spinning but non-precessing black holes, for the same accuracy, local hp-greedy reduced bases with HPO have a lower dimensionality of up to 4×, depending on the desired accuracy. This factor should directly translate into a parameter estimation speedup in the context of reduced order quadratures, for instance. Such acceleration might help in the near real-time requirements for electromagnetic counterparts of gravitational waves from compact binary coalescences. The code developed for this project is available open source from public repositories. This paper is an invited contribution to the Special Issue “Recent Advances in Gravity: A Themed Issue in Honor of Prof. Jorge Pullin on his 60th Anniversary”.

Algorithm to determine local basis weight of random fibrous networks with X-ray microtomography and SEM images

Analysis of the basis weight for random fibrous networks is important to understand their microstructure, properties and performance. Two-dimensional microscopical images show in-plane fibers without giving any information on their distribution in three dimensions. This research introduces a fully parametric algorithm for computing the local basis weight of random fibrous networks using three-dimensional images because out-of-plane fiber orientation is important, especially for high-density or thick networks. Voxel models of real nonwoven webs were generated by an X-ray micro-computed tomography system. The developed algorithm could accurately estimate a local basis weight value for random fibrous networks produced with various manufacturing parameters. Numerical results computed with the developed method were compared with those obtained with a physical weight measurement technique. The algorithm was tested and validated for various nonwoven fabrics with different densities. It was observed that the developed method can be used to examine and/or compare the basis weight of a wide range of random fibrous networks. In addition, it can be used to predict the basis weight for fabrics, especially in a new product development process.

Representability of relatively free affine algebras over a Noetherian ring

Over the years questions have arisen about T-ideals of (noncommutative) polynomials. But when evaluating a noncentral polynomial in subalgebras of matrices, one often has little control in determining the specific evaluations of the polynomial. One way of overcoming this difficulty in characteristic 0, is to reduce to multilinear polynomials and to utilize the representation theory of the symmetric group. But this technique is unavailable in characteristic [Formula: see text]. An alternative method, which succeeds, is the process of “hiking” a polynomial, in which one specializes its indeterminates in several stages, to obtain a polynomial in which Capelli polynomial is embedded, in order to get control on its evaluations. This method was utilized on homogeneous polynomials in the proof of Specht’s conjecture for affine algebras over fields of positive characteristic. In this paper, we develop hiking further to nonhomogeneous polynomials, to apply to the “representability question.” Kemer proved in 1988 that every affine relatively free PI algebra over an infinite field, is representable. In 2010, the first author of this paper proved more generally that every affine relatively free PI algebra over any commutative Noetherian unital ring is representable [A. Belov, Local finite basis property and local representability of varieties of associative rings, Izv. Russian Acad. Sci. (1) (2010) 3–134. English Translation Izv. Math. 74(1) (2010) 1–126]. We present a different, complete, proof, based on hiking nonhomogeneous polynomials, over finite fields. We then obtain the full result over a Noetherian commutative ring, using Noetherian induction on T-ideals. The bulk of the proof is for the case of a base field of positive characteristic. Here, whereas the usage of hiking is more direct than in proving Specht’s conjecture, one must consider nonhomogeneous polynomials when the base ring is finite, which entails certain difficulties to be overcome. In Appendix A, we show how hiking can be adapted to prove the involutory versions, as well as various graded and nonassociative theorems.

An adaptive support domain for the in-compressible fluid flow based on the localized radial basis function collocation method

In this paper, an adaptive support domain scheme is proposed to the in-compressible fluid flow based on the localized radial basis function collocation method (LRBFCM). The idea of the adaptive support domain avoids complex mathematical derivations of the finite difference method (FDM). Unlike other upwind schemes in the LRBFCM, the support domain uses the sampling nodes similar to different finite difference schemes, and the improved LRBFCM is further applied to the in-compressible fluid flows. Considering the Kronecker tensor product and Cholesky decomposition techniques, the improved LRBFCM can be easily used to the lid-driven problems with Reynolds numbers up to 100,000 by a simple mathematical derivation. The proposed LRBFCM has an adaptive support domain similar to the finite difference schemes with much less CPU time costs.

Effect of graphene grating coating on near-field radiative heat transfer

In this work, we analyze the near-field radiative heat transfer (NFRHT) between finite-thickness planar fused silica slabs coated with graphene gratings. We go beyond the effective medium approximation by using an exact Fourier modal method equipped with specific local basis functions, and this is needed for realistic experimental analysis. In general, coating a substrate with a full graphene sheet has been shown to decrease the NFRHT at short separations (typically for d < 100 nm) compared to the bare substrates, where the effective medium approximation consistently overestimates the radiative heat flux, with relative errors exceeding 50%. We show that by patterning the graphene sheet into a grating, the topology of the plasmonic graphene mode changes from circular to hyperbolic, allowing to open more channels for the energy transfer between the substrates. We show that at short separations, the NFRHT between slabs coated with graphene gratings is higher than that between full-graphene-sheet coated slabs and also than that between uncoated ones. We also exhibit a significant dependence of the radiative heat transfer on the chemical potential, which can be applied to modulate in situ the scattering properties of the graphene grating without any geometric alterations. Additionally, we compare the exact calculation with an approximate additive one and confirm that this approximation performs quite well for low chemical potentials. This work has the potential to unveil new avenues for harnessing non-additive heat transfer effects in graphene-based nanodevices.

On the genesis of the bow designs from the “Old Buryat” burials

In the paper, the finds of fragments of bows from the “Old Buryat” burials of the 17th–18th centuries from the Baikal region are analysed, and an attempt is made to determine their genesis from the data on their technological features. On the basis of the conventional method of weapon-analysis classification, two types were distinguished by the set of the reinforcing onlays. To understand the missing structural elements, the data is drawn in on more recent fully preserved items produced locally in the 19th — early 20th c. from the museum and private collections from the territory of the Baikal region, since a genetic affinity can be traced between them and the earlier products by the available onlays. This allows one to speak about similar morphological and metric characteristics between the Buryat bows of the 19th — early 20th c. and the objects from the “Old Buryat” burials. In the result of the conducted analysis, the relationship between the distinguished type 1 and items of the 12th–14th cc. of the population of the Ust-Talkinskaya Culture of the Cisbaikalia region has been established by the onlays used and the structure of the wooden base (in comparison with the products of the Buryats of the 17th–18th cc. associated with the bows of the 19th — early 20th c.), on the basis of which it was concluded that the design evolved in the Mongolian period from a local prototype. The type 2 is also associated with ‘Mongolian type’ bows by the presence of the median frontal remiform onlay, although it has the features of Yakut’s ‘Central Asian’ bows (the end frontal straps made of staghorn with a wide and a narrow areas). In the course of the study, it has been revealed that the design of the objects of the 19th — early 20th c., predominantly Transbai-kalian bows of the Selenga Buryats, has features of both the type 1 as well as the type 2, and it evolved from a local basis as a result of the synthesis of the elements of these types, thus combining the features of the northern and local workmanships. In the result, the structures appeared, which were reinforced with long end straps made of staghorn, with a long wide area creating transitional zones, and a short narrow one reinforcing the rigid limb tips. In the Cisbaikalia region, modifications of the type 1 bow were further developed by means of combining materials in the onlays of the transitional zones. All of the recorded bows, in terms of the shape of the ends and transitional zones, are much closer to the Mongolian bows of the 12th–14th c. from the rock burials of Mongolia, than to the Manchurian-Mongolian bows widespread in Central Asia since the 17th c.

Node-bound communities for partition of unity interpolation on graphs

Graph signal processing benefits significantly from the direct and highly adaptable supplementary techniques offered by partition of unity methods (PUMs) on graphs. In our approach, we demonstrate the generation of a partition of unity solely based on the underlying graph structure, employing an algorithm that relies exclusively on centrality measures and modularity, without requiring the input of the number of subdomains. Subsequently, we integrate PUMs with a local graph basis function (GBF) approximation method to develop cost-effective global interpolation schemes. We also discuss numerical experiments conducted on both synthetic and real datasets to assess the performance of this presented technique.

Shift Current with Gaussian Basis Sets and General Prescription for Maximally Symmetric Summations in the Irreducible Brillouin Zone.

The bulk photovoltaic effect is an experimentally verified phenomenon by which a direct charge current is induced within a non-centrosymmetric material by light illumination. Calculations of its intrinsic contribution, the shift current, are nowadays amenable from first-principles employing plane-wave bases. In this work, we present a general method for evaluating the shift conductivity in the framework of localized Gaussian basis sets that can be employed in both the length and velocity gauges, carrying the idiosyncrasies of the quantum-chemistry approach. The (possibly magnetic) symmetry of the system is exploited in order to fold the reciprocal space summations to the representation domain, allowing us to reduce computation time and unveiling the complete symmetry properties of the conductivity tensor under general light polarization.

On the eigenvalue distribution of spatio-spectral limiting operators in higher dimensions

Prolate spheroidal wave functions are an orthogonal family of bandlimited functions on R that have the highest concentration within a specific time interval. They are also identified as the eigenfunctions of a time-frequency limiting operator (TFLO), and the associated eigenvalues belong to the interval [0,1]. Previous work has studied the asymptotic distribution and clustering behavior of the TFLO eigenvalues.In this paper, we extend these results to multiple dimensions. We prove estimates on the eigenvalues of a spatio-spectral limiting operator (SSLO) on L2(Rd), which is an alternating product of projection operators associated to given spatial and frequency domains in Rd. If one of the domains is a hypercube, and the other domain is convex body satisfying a symmetry condition, we derive quantitative bounds on the distribution of the SSLO eigenvalues in the interval [0,1].To prove our results, we design an orthonormal system of wave packets in L2(Rd) that are highly concentrated in the spatial and frequency domains. We show that these wave packets are “approximate eigenfunctions” of a spatio-spectral limiting operator. To construct the wave packets, we use a variant of the Coifman-Meyer local sine basis for L2[0,1], and we lift the basis to higher dimensions using a tensor product.