Journal articles: 'Geometrical Partition'

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DOREY, PATRICK. "PARTITION FUNCTIONS, INTERTWINERS AND THE COXETER ELEMENT." International Journal of Modern Physics A 08, no. 01 (January 10, 1993): 193–208. http://dx.doi.org/10.1142/s0217751x93000084.

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The partition functions of Pasquier models on the cylinder, and the associated intertwiners, are considered. It is shown that earlier results due to Saleur and Bauer can be rephrased in a geometrical way, reminiscent of formulae found in certain purely elastic scattering theories. This establishes the positivity of these intertwiners in a general way and elucidates connections between these objects and the finite subgroups of SU(2). It also offers the hope that analogous geometrical structures might lie behind the so-far mysterious results found by DiFrancesco and Zuber in their search for generalisations of these models.

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Yang, Zeng-hui. "On-the-fly determination of active region centers in adaptive-partitioning QM/MM." Physical Chemistry Chemical Physics 22, no. 34 (2020): 19307–17. http://dx.doi.org/10.1039/d0cp03034a.

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Rivier, N., E. Guyon, and E. Charlaix. "A geometrical approach to percolation through random fractured rocks." Geological Magazine 122, no. 2 (March 1985): 157–62. http://dx.doi.org/10.1017/s001675680003106x.

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AbstractThe permeability of rocks fractured by random, planar cracks, is expressed as a classical bond percolation problem on a random lattice, by Voronoi partition of space. The percolation threshold is determined as a function of the statistical characteristics of the cracks, or of their traces on an arbitrary face of the rock, by using an empirical quasi-invariant of percolation theory.

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Chen, Jie, and Jun Ting Cheng. "An Improved Method of the Adaptive Hierarchical Space Partition Simplification Algorithm on the Point-Based Model." Advanced Materials Research 915-916 (April 2014): 1259–65. http://dx.doi.org/10.4028/www.scientific.net/amr.915-916.1259.

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The 3D scanning device can capture millions of points with the excellent geometrical precision except for large amount of redundant ones, which could bring some difficulties for the subsequent digital geometrical processing (DGP), so the simplification of the point cloud has become a considerable study in point cloud applications. Given this problem, we propose a novel approach, which could decrease the geometrical error by partitioning the surface into many patches with some similar geometrical features before using the adaptive hierarchical space partition (AHSP) approach, in order to improve the AHSP simplification. We also experiment on three models and do comparative analysis. Fortunately, the results prove that our algorithm can make the anisotropy feature in the surface of the models described explicitly, the geometrical error decreased by 15.8 percent, and the simplification rate kept up with other approaches. In addition, it can provide the high quality models for the 3D digital model editing, such as the geometrical modeling, the point cloud blending.

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HOLUB, ŠTĚPÁN, and JUHA KORTELAINEN. "ON PARTITIONS SEPARATING WORDS." International Journal of Algebra and Computation 21, no. 08 (December 2011): 1305–16. http://dx.doi.org/10.1142/s0218196711006650.

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Partitions [Formula: see text] of A+ into m pairwise disjoint languages L1, L2, …, Lm such that [Formula: see text] for k = 1, 2, …, m are considered. It is proved that such a closed partition of A+ can separate the words u1, u2, …, um ∈ A+ (i.e., each Lk contains exactly one word of the sequence u1, u2, …, um) if and only if for each pair i, j of distinct elements in {1, 2, …, m}, the words ui and uj do not commute. Furthermore, it is proved that the separating languages can be chosen to be regular. In case that the Parikh images of the words are linearly independent, the choice of the separating languages may be based on geometrical intuition.

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MIGUET, SERGE, and JEAN-MARC PIERSON. "QUALITY AND COMPLEXITY BOUNDS OF LOAD BALANCING ALGORITHMS FOR PARALLEL IMAGE PROCESSING." International Journal of Pattern Recognition and Artificial Intelligence 14, no. 04 (June 2000): 463–76. http://dx.doi.org/10.1142/s0218001400000301.

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The parallel implementation of image processing algorithms implies an important choice of data distribution strategy. In order to handle the specific constraints associated with images, data distribution must take into account not only the locality of the data and its geometrical regularity but also the possible irregular computation costs associated with different image elements. A widely studied field to tackle this problem is the family of methods related to rectilinear partitioning. We introduce two fully parallel heuristics that compute suboptimal partitions, with a better complexity than the best known algorithms that compute optimal partitions. In this paper, we compare our heuristics to an optimal partitioning, both in terms of execution time and accuracy of the partition. We give some theoretical bounds on the quality of these heuristics that are corroborated by results of random numerical experiments and real applications.

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CARFORA, M., M. MARTELLINI, and A. MARZUOLI. "COMBINATORIAL AND TOPOLOGICAL PHASE STRUCTURE OF NON-PERTURBATIVE n-DIMENSIONAL QUANTUM GRAVITY." International Journal of Modern Physics B 06, no. 11n12 (June 1992): 2109–21. http://dx.doi.org/10.1142/s0217979292001055.

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We provide a non-perturbative geometrical characterization of the partition function of ndimensional quantum gravity based on a rough classification of Riemannian geometries. We show that, under natural geometrical constraints, the theory admits a continuum limit with a non-trivial phase structure parametrized by the homotopy types of the class of manifolds considered. The results obtained qualitatively coincide, when specialized to dimension two, with those of two-dimensional quantum gravity models based on random triangulations of surfaces.

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Hosseini-Toudeshky, H., M. R. Mofakhami, and R. Yarmohammadi. "Sound transmission between partitioned contiguous enclosures." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 223, no. 5 (February 4, 2009): 1091–101. http://dx.doi.org/10.1243/09544062jmes1166.

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By increasing the application of lightweight constructions, sound transmission between the adjacent enclosures becomes a more important consideration in designing new buildings. In this article, the parameters that may significantly affect the sound transmission level through a partition between two adjacent enclosures are investigated, i.e. geometrical dimensions, arrangement of enclosures, boundary conditions, multi-layered partitions, and framed (or reinforced) conditions of the partitions. For this purpose, sound transmission is modelled using the finite-element method. The obtained results from sound transmission using Perspex party walls with different width and boundary conditions are compared with those obtained from a double-layered wall with an air layer. The effects of an enclosure's arrangements and dimensions on sound transmission of the party walls are also studied. Using the cross-framed party wall causes more noise reduction than the double-layered party wall. The results also show that sound transmission between rooms with an asymmetric arrangement is less than that obtained from a symmetric configuration.

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Hatzinikitas, Agapitos N. "The Partition Function of the Dirichlet OperatorD2s=∑i=1d‍(-∂i2)son ad-Dimensional Rectangle Cavity." Journal of Mathematics 2015 (2015): 1–7. http://dx.doi.org/10.1155/2015/785720.

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We study the asymptotic behavior of the free partition function in thet→0+limit for a diffusion process which consists ofd-independent, one-dimensional, symmetric,2s-stable processes in a hyperrectangular cavityK⊂Rdwith an absorbing boundary. Each term of the partition function for this polyhedron ind-dimensions can be represented by a quermassintegral and the geometrical information conveyed by the eigenvalues of the fractional Dirichlet Laplacian for this solvable model is now transparent. We also utilize the intriguing method of images to solve the same problem, in one and two dimensions, and recover identical results to those derived in the previous analysis.

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Pathak, Himanshu, Akhilendra Singh, and Indra Vir Singh. "Composite Patch Repair of Structural Member by Coupled FE-EFG Approach." Applied Mechanics and Materials 829 (March 2016): 78–82. http://dx.doi.org/10.4028/www.scientific.net/amm.829.78.

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This paper presents a simple and efficient coupled finite element-element free Galekrin (FE-EFG) approach to simulate three-dimensional composite patch repair problem. In coupled FE-EFG approach, extended element free Galerkin (XEFG) is used near the crack surface as it can accurately model the discontinuities while the rest of domain is approximated by standard finite element (FE) method. The transition between FE and XEFG was modelled by a ramp function. The geometric discontinuities like crack and material interface are modeled by adding enrichment functions in EFG displacement approximation through partition of unity (PU). The location of geometrical discontinuity is traced by vector level set method. A domain based J-integral approach is used for the evaluation of stress intensity factors.

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GATTRINGER, C. R., S. JAIMUNGAL, and G. W. SEMENOFF. "LOOPS, SURFACES AND GRASSMANN REPRESENTATION IN TWO- AND THREE-DIMENSIONAL ISING MODELS." International Journal of Modern Physics A 14, no. 29 (November 20, 1999): 4549–74. http://dx.doi.org/10.1142/s0217751x9900213x.

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We construct an algebraic representation of the geometrical objects (loop and surface variables) dual to the spins in 2 and 3D Ising models. This algebraic calculus is simpler than dealing with the geometrical objects, in particular when analyzing geometry factors and counting problems. For the 2D case we give the corrected loop expansion of the free energy and the radius of convergence for this series. For the 3D case we give a simple derivation of the geometry factor which prevents overcounting of surfaces in the intrinsic geometry representation of the partition function, and find a classification of the surfaces to be summed over. For 2 and 3D we derive a compact formula for 2n-point functions in loop (surface) representation.

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Song, Yunsheng, Jiye Liang, and Feng Wang. "An accelerator for support vector machines based on the local geometrical information and data partition." International Journal of Machine Learning and Cybernetics 10, no. 9 (October 9, 2018): 2389–400. http://dx.doi.org/10.1007/s13042-018-0877-7.

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RUSAKOV, B. YE. "LOOP AVERAGES AND PARTITION FUNCTIONS IN U(N) GAUGE THEORY ON TWO-DIMENSIONAL MANIFOLDS." Modern Physics Letters A 05, no. 09 (April 10, 1990): 693–703. http://dx.doi.org/10.1142/s0217732390000780.

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Loop averages and partition functions in the U(N) gauge theory are calculated for loops without intersections on arbitrary two-dimensional manifolds including nonorientable ones. The physical quantities are directly expressed through geometrical characteristics of a manifold (areas enclosed by loops and the genus) and gauge group parameters (Casimir eigenvalues and dimensions of the irreducible representations). It is shown that, from the physical quantities’ point of view, non-orientability of the manifold is equivalent to its non-compactness.

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DOUGHERTY, RANDALL. "OPEN SETS SATISFYING SYSTEMS OF CONGRUENCES." Journal of Mathematical Logic 01, no. 02 (November 2001): 247–303. http://dx.doi.org/10.1142/s0219061301000107.

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A famous result of Hausdorff states that a sphere with countably many points removed can be partitioned into three pieces A, B, C such that A is congruent to B (i.e. there is an isometry of the sphere which sends A to B), B is congruent to C, and A is congruent to B ∪ C; this result was the precursor of the Banach–Tarski paradox. Later, R. Robinson characterized the systems of congruences like this which could be realized by partitions of the (entire) sphere with rotations witnessing the congruences. The pieces involved were nonmeasurable. In the present paper, we consider the problem of which systems of congruences can be satisfied using open subsets of the sphere (or related spaces); of course, these open sets cannot form a partition of the sphere, but they can be required to cover "most of" the sphere in the sense that their union is dense. Various versions of the problem arise, depending on whether one uses all isometries of the sphere or restricts oneself to a free group of rotations (the latter version generalizes to many other suitable spaces), or whether one omits the requirement that the open sets have dense union, and so on. While some cases of these problems are solved by simple geometrical dissections, others involve complicated iterative constructions and/or results from the theory of free groups. Many interesting questions remain open.

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Alturria Lanzardo, C. J., J. E. Pérez, M. L. Tardivo, G. Fraschetti, and J. C. Cesco. "A New Expression for the Coulomb Potential Corresponding to the Product of Two Exponential Functions Based on the Properties of the Integral Representations of the Bessel Functions." Trends in Computational and Applied Mathematics 24, no. 1 (March 14, 2023): 1–7. http://dx.doi.org/10.5540/tcam.2022.024.01.00001.

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The calculation of the Coulomb Potential corresponding to the product of two Exponential Type Functions, inherently has numerical challenges that must be resolved. In order to address these problems, in this paper it is presented a new partition of the Coulomb Potential. The proposed partition involves two terms. One of the terms is a one-dimensional integral, which allows geometrical and statistical interpretations. The other term is proportional to a Modified Bessel Function and it is obtained from a two-step procedure. As a first step, a Non-Rational Function is used for approximating one of the two integrals involved. Then, the remaining improper integral can be identified with an integral representation of an appropriate Modified Bessel Function. The existence of such a Non-Rational Approximant is proved and its numerical performance is shown through some examples.

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Xu, Hui Ying, Jian Wei Zou, and Wei Wang. "Prediction of Soot-Water Partition Coefficients for Persistent Organic Pollutants." Advanced Materials Research 518-523 (May 2012): 2677–81. http://dx.doi.org/10.4028/www.scientific.net/amr.518-523.2677.

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In the present study, geometrical optimization and electrostatic potential calculations have been performed at the HF/6-31G* level of theory for 25 investigated persistent organic pollutants (POPs), including ten polychlorinated dibenzo-p-dioxins and dibenzofurans (PCDD/Fs), nine polychlorinated biphenyls (PCBs), four polycyclic aromatic hydrocarbons (PAHs) and two polybrominated diphenyl ethers (PBDEs). A number of statistically-based parameters have been obtained. Linear relationships between soot–water partition coefficients (log KSC) of POPs and the structural descriptors have been established by multiple linear regression method. The result shows that the quantities derived from electrostatic potential, together with molecular surface area (AS) and the energy of the highest occupied molecular orbital (EHOMO) can be well used to express the quantitative relationships between structure and soot–water partition coefficients of POPs. Predictive capability of the model has been demonstrated by leave-one-out cross-validation with the cross-validated correlation coefficient (RCV) of 0.9797. Furthermore, the predictive power of this model was further examined for the external test set. The QSPR model established may provide a new powerful method for predicting soot–water partition coefficients (KSC) of persistent organic pollutants.

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Liu, Zhihong, Xilong Zhang, Zunmin Liu, Chuijie Yi, and Ming Ma. "A Partition Spatial Filtering Method for Acoustic Array Configuration." Shock and Vibration 2021 (February 11, 2021): 1–18. http://dx.doi.org/10.1155/2021/6682923.

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Acoustic array is a ubiquitous tool for locating and quantifying sound sources. However, its effectiveness depends greatly on the array configuration. This paper presents an array configuration method to enhance array performance, especially on the spatial resolution and the Doppler effect correction. The problem of array configuration is formulated into a position matrix determined by introducing partition spatial filtering. Irregular coaxial ring grid spacings and partition filtering conditions are suggested to control array spatial resolution. Geometrical parameters and performance indicators are constructed to quantify the relationships between the array configuration and performance. Based on these quantitative relations, the spatial variation of the array beam pattern and the Doppler effect has got adaptive adjustment. In particular, an adaptive partition algorithm is proposed to reduce computation time. The performance of the method is examined numerically and experimentally, which is compared with the other methods. The results provide the method to guide the design of a 64-microphone optimized array with high performance (1.8° spatial angle resolution and 40% Doppler frequency correction over the bandwidth from 800 Hz to 3000 Hz) and fast computing speed (18 s array generated time for 2000 arrays). Furthermore, an unusual feature of the method is that it can be utilized in the case when the source moves at a nonconstant velocity.

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van Ravenstein, Tony. "The Three Gap Theorem (Steinhaus Conjecture)." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 45, no. 3 (December 1988): 360–70. http://dx.doi.org/10.1017/s1446788700031062.

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AbstractThis paper is concerned with the distribution of N points placed consecutively around the circle by an angle of α. We offer a new proof of the Steinhaus Conjecture which states that, for all irrational α and all N, the points partition the circle into arcs or gaps of at least two, and at most three, different lengths. We then investigate the partitioning of a gap as more points are included on the circle. The analysis leads to an interesting geometrical interpretation of the simple continued fraction expansion of α.

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Muñoz, Ricardo C. "Combined Diagram: A Graphical Representation of Combination Evaporation Rates." Journal of Hydrometeorology 13, no. 4 (August 1, 2012): 1389–95. http://dx.doi.org/10.1175/jhm-d-12-05.1.

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Abstract Combination methods estimate the partition of sensible and latent heat fluxes at the surface by combining the surface energy balance equation with the transfer equations for temperature and water vapor in the atmospheric surface layer. This paper presents a diagram that graphically depicts the main assumptions and steps of the method. Potential, apparent potential, and actual evaporation rates are visually explained with the diagram. Using a linearized saturation water content relation, the diagram permits the derivation of many of the combination evaporation results by means of geometrical analysis. The diagram should be helpful in the teaching and understanding of the combination methodology.

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Halle, Willi, Ingo Baeger, Björn Ekwall, and Horst Spielmann. "Correlation between In Vitro Cytotoxicity and Octanol/Water Partition Coefficient of 29 Substances from the MEIC Programme." Alternatives to Laboratory Animals 19, no. 3 (July 1991): 338–43. http://dx.doi.org/10.1177/026119299101900307.

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Single linear regression analysis was used for chemicals of the MEIC (multicentre evaluation of in vitro cytotoxicity) project, to obtain a correlation between in vitro cytotoxicity determined in various test systems, according to data from the literature, and their lipophilicity. A linear correlation coefficient of 0.76 was determined between the IC50x¯ values (geometrical mean of two or more IC50 values per substance) of 29 MEIC substances and their octanol/water partition coefficient (owp). Since the MEIC substances were selected from a broad spectrum of structurally unrelated classes of chemicals, it may be possible to make close predictions of the general in vitro cytotoxicities of chemicals from their owp coefficients.

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Obikawa, Toshiyuki, and J. Shinozuka. "Analysis of Grinding Temperature Considering Surface Generation Mechanism." Key Engineering Materials 291-292 (August 2005): 97–102. http://dx.doi.org/10.4028/www.scientific.net/kem.291-292.97.

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Grinding temperature was analyzed considering heat generation by cutting with each abrasive on the wheel working periphery. A geometrical analysis of interference between the abrasives and workpiece gave the instantaneous cutting cross section, and visualized the surface topography generated by the time. Using the specific grinding energy and the instantaneous cutting cross sections, the instantaneous distribution of heat generation on the wheel-workpiece contact area was obtained. Then grinding temperature was calculated for a given heat partition into the workpiece. Since a cutting with an abrasive generated an impulse of heat flux, temperature distribution calculated for grinding carbon tool steel varied drastically, and very high local temperature or temperature spikes appeared.

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López-Sauceda, Juan, Jorge López-Ortega, Gerardo Laguna Sánchez, Jacobo Sandoval Gutiérrez, Ana Rojas Meza, and José Aragón. "Spatial Organization of Five-Fold Morphology as a Source of Geometrical Constraint in Biology." Entropy 20, no. 9 (September 14, 2018): 705. http://dx.doi.org/10.3390/e20090705.

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A basic pattern in the body plan architecture of many animals, plants and some molecular and cellular systems is five-part units. This pattern has been understood as a result of genetic blueprints in development and as a widely conserved evolutionary character. Despite some efforts, a definitive explanation of the abundance of pentagonal symmetry at so many levels of complexity is still missing. Based on both, a computational platform and a statistical spatial organization argument, we show that five-fold morphology is substantially different from other abundant symmetries like three-fold, four-fold and six-fold symmetries in terms of spatial interacting elements. We develop a measuring system to determine levels of spatial organization in 2D polygons (homogeneous or heterogeneous partition of defined areas) based on principles of regularity in a morphospace. We found that spatial organization of five-fold symmetry is statistically higher than all other symmetries studied here (3 to 10-fold symmetries) in terms of spatial homogeneity. The significance of our findings is based on the statistical constancy of geometrical constraints derived from spatial organization of shapes, beyond the material or complexity level of the many different systems where pentagonal symmetry occurs.

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Basak, Subhash C., Brian D. Gute, and Gregory D. Grunwald. "A Comparative Study of Topological and Geometrical Parameters in Estimating Normal Boiling Point and Octanol/Water Partition Coefficient." Journal of Chemical Information and Computer Sciences 36, no. 6 (January 1996): 1054–60. http://dx.doi.org/10.1021/ci960024i.

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Alata, O., S. Burg, and A. Dupas. "Grouping/degrouping point process, a point process driven by geometrical and topological properties of a partition in regions." Computer Vision and Image Understanding 115, no. 9 (September 2011): 1324–39. http://dx.doi.org/10.1016/j.cviu.2011.05.003.

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ZHOU, H., E. PERFECT, Y. Z. LU, B. G. LI, and X. H. PENG. "MULTIFRACTAL ANALYSES OF GRAYSCALE AND BINARY SOIL THIN SECTION IMAGES." Fractals 19, no. 03 (September 2011): 299–309. http://dx.doi.org/10.1142/s0218348x11005403.

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Multifractal analyses of binary images of soil thin sections (STS) are widely used to characterize pore structure. However, no geometrical model is known to exist for a binary multifractal. Thus, the multifractality of binary images, and the accuracy of multifractal parameters estimated from them, need to be carefully evaluated. We captured 8-bit depth resolution digital grayscale images of three STS images with dimensions of 1024 × 1024 pixels and a pixel length of 1.9 μm. Random grayscale geometrical multifractal fields (GMF) with similar dimensions and known multifractal parameters were constructed using generators extracted from the STS images. The STS and GMF grayscale images were objectively thresholded to give six binary images. The method of moments was used to compute the log-transformed partition function, log (χ(q, δ)) versus log(δ) where δ is box size, for each grayscale image and its binary counterpart. Consistent linearity was observed in the resulting functions for the grayscale images, indicating, by definition, multifractal behavior. In contrast, the log (χ(q, δ)) versus log(δ) plots for the binary images exhibited a two-region response, with a flat plateau at small scales and linearity at larger scales, indicating they were not true multifractals. Generalized dimensions (Dq) computed from the linear portions of the binary log-transformed partition functions were significantly over estimated for q ≪ 0 and underestimated for q ≫ 0 relative to corresponding Dq values for the grayscale images. Based on these results we contend that binary images are not mathematical multifractals, and that generalized dimensions estimated from them cannot be used to quantify pore space geometry. Instead we encourage further exploration of the use of grayscale images for multifractal characterization of soil structure. This direct approach is theoretically sound and does not require any intermediate thresholding step, which is known to influence the results of multifractal analyses.

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SAVVIDY, G. K., and K. G. SAVVIDY. "STRING FINE-TUNING." International Journal of Modern Physics A 08, no. 22 (September 10, 1993): 3993–4011. http://dx.doi.org/10.1142/s0217751x93001624.

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We develop further a new geometrical model of a discretized string, proposed in Ref. 1, and establish its basic physical properties. The model can be considered as the natural extension of the usual Feynman amplitude of the random walks to random surfaces. Both amplitudes coincide in the case, when the surface degenerates into a single particle world line. We extend the model to open surfaces as well. The boundary contribution is proportional to the full length of the boundary, and the coefficient of proportionality can be treated as a hopping parameter of the quarks. In the limit when this parameter tends to infinity, the theory is essentially simplified. We prove that the contribution of a given triangulation to the partition function is finite and have found the explicit form for the upper bound. The question of the convergence of the full partition function remains open. In this model the string tension may vanish at the critical point, if the last one exists, and possesses a nontrivial scaling limit. The model contains hidden fermionic variables and can be considered as an independent model of hadrons.

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Borysenko, Oksana, Sergii Logvinkov, Halyna Shabanova, Igor Остапенко, and Vita Шумейко. "GEOMETRICAL–TOPOLOGICAL CHARACTERISTICS OF THE SUBSOLIDUS STRUCTURE IN THE MgO – Al2O3 – TiO2 SYSTEM." Bulletin of the National Technical University "KhPI". Series: Chemistry, Chemical Technology and Ecology, no. 1(5) (May 15, 2021): 18–23. http://dx.doi.org/10.20998/2079-0821.2021.01.03.

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Among the materials that attract attention from the point of view of creating refractory products with increased heat resistance, one can single out materials based on compositions of the MgO – Al2O3 – TiO2 system. As a result of the thermodynamic analysis of the MgO – Al2O3 – TiO2 system, it was found that the partition of the system into elementary triangles will change in three temperature ranges: I – up to 1537 K, II – in the temperature range 1537 – 2076 K and above 2076 K. It has been established that up to a temperature of 2076 K there is a concentration range of spinel phases: magnesium aluminate spinel – quandylite. Above 1537 K, there is a concentration range: tialite – karroite, which meets the requirements for materials with high heat resistance. The elementary triangle TiO2 – Al2TiO5 – MgTi2O5 can be used to obtain heat–resistant materials based on Al2TiO5 stabilized by MgTi2O5. To obtain heat–resistant periclase–spinel materials, an elementary triangle Mg2TiO4 – MgAl2O4 – MgO is recommended, in which only compounds with a cubic crystal lattice are present. Thus, the division of the MgO – Al2O3 – TiO2 system into elementary triangles and the analysis of the geometrical–topological characteristics of the phases of the system made it possible to select in the system under study the regions of compositions that have optimal properties for obtaining materials with the specified optimal properties.

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Ma, Suqi. "Hopf Bifurcation of a Type of Neuron Model with Multiple Time Delays." International Journal of Bifurcation and Chaos 29, no. 12 (November 2019): 1950163. http://dx.doi.org/10.1142/s0218127419501633.

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By applying a geometrical scheme developed to tackle the eigenvalue problem of delay differential equations with multiple time delays, Hopf bifurcation of Hopfield neuron model is analyzed in two-parameter space. By the introduction of two new angles, the calculation of imaginary roots is carried out analytically and effectively. By increasing the parameter to cross over the Hopf bifurcation lines, the stability switching direction is confirmed. The method is a useful tool to show the partition of stable and unstable regions in two-parameter space and detect double Hopf bifurcation further. The typified dynamical behaviors based on nearby double Hopf points are analyzed by applying the normal form technique and center manifold method.

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MAIER, R., and I. DAMIÃO SOARES. "GRAVITATIONAL COLLAPSE AND BLACK HOLE THERMODYNAMICS IN BRANEWORLD SCENARIO." International Journal of Modern Physics D 21, no. 05 (May 2012): 1250050. http://dx.doi.org/10.1142/s0218271812500502.

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We examine the dynamics of the gravitational collapse in a 4-dim Lorentzian brane embedded in a 5-dim bulk with an extra timelike dimension. By considering the collapse of pure dust on the brane we derive a bouncing FLRW interior solution and match it with a corrected Schwarzschild exterior geometry. In the physical domain considered for the parameters of the solution, the analytical extension is built, exhibiting an exterior event horizon and a Cauchy horizon, analogous to the Reissner–Nordstrom solution. For such an exterior geometry we examine the effects of the bulk-brane corrections in the Hawking radiation. In this scenario the model extends Bekenstein's black hole geometrical thermodynamics for quasi-extremal configurations, with an extra work term in the laws associated with variations of the brane tension. We also propose a simple statistical mechanics model for the entropy of the bouncing collapsed matter by quantizing its fluctuations and constructing the associated partition function. This entropy differs from the geometrical entropy by an additive constant proportional to the area of the extremal black hole and satisfies an analogous first law of thermodynamics. A possible connection between both entropies is discussed.

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Wang, Cai Yin, Jun Sheng Cai, and Ming Jie Zhen. "An Information Hiding Method in Presswork Based on Image Complexity and Template Matching." Applied Mechanics and Materials 321-324 (June 2013): 2635–38. http://dx.doi.org/10.4028/www.scientific.net/amm.321-324.2635.

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This paper proposes an information hiding method in presswork based on image and complexity and template matching. First, the message to be hidden is coded by using BCH to facilitate the extraction of hidden information. Secondly, Based on appropriate image block partition, the local image complexity of the block is calculated, which is determined whether to embed watermark in this block. Watermark is embedded on the mid-frequency spectrum in DFT domain. Thirdly, two structural template lines are added in the polar coordinate system for detecting any combination of the geometrical distortions. Then, the hidden data can be extracted without using the original image. The experimental results indicate that the proposed method is robust after high-quality laser printing, offset printing and scanning.

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GERASIMOV, A., YU MAKEENKO, A. MARSHAKOV, A. MIRONOV, A. MOROZOV, and A. ORLOV. "MATRIX MODELS AS INTEGRABLE SYSTEMS: FROM UNIVERSALITY TO GEOMETRODYNAMICAL PRINCIPLE OF STRING THEORY." Modern Physics Letters A 06, no. 33 (October 30, 1991): 3079–90. http://dx.doi.org/10.1142/s0217732391003572.

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Matrix models are equivalent to certain integrable theories, partition functions being equal to certain τ-functions, i.e., the section of determinant bundles over infinite-dimensional Grassmannian. These τ-functions are evaluated at the points of Grassmannian, where high symmetry arises. In the case of one-matrix models the symmetry is isomorphic to Borel subgroup of a Virasoro group. The orbits of the group are in one-to-one correspondence with the types of "multicritical" behavior in the continuum limit. Interrelation between τ-functions in different models and their continuum limit is discussed in some details. We also discuss the implications for dynamical interpolation between various string models (CFT's), to be described in terms of geometrical quantization of Fairlie-like [Formula: see text]-algebras.

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Zhu, Jian Qing, Wei Wang, and Hui Ying Xu. "QSPR Models for the Physicochemical Properties of Polychlorinated Naphthalene Congeners." Advanced Materials Research 726-731 (August 2013): 440–43. http://dx.doi.org/10.4028/www.scientific.net/amr.726-731.440.

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Based on quantitative structureproperty relationship (QSPR) of organic compounds, geometrical optimization and quantum chemical parameter calculations have been performed at the B3LYP/6-31G* level of theory for 75 polychlorinated naphthalenes (PCNs). A number of statistically-based parameters have been obtained. Relationship between the physicochemical properties of polychlorinated naphthalene compounds (n-octanol/air partition coefficient, sub-cooled liquid vapor pressure, water solubility) and the structural descriptors have been established by multiple linear regression (MLR) method. The results show that the molecular volume (Vmc), dipolar moment (μ), and the energy of lowest unoccupied molecular orbital (ELUMO), together with the quantity derived from electrostatic potential () can be well used to express the quantitative structure-property relationships of polychlorinated naphthalene compounds. The models constructed have good robustness and high predictive capability.

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Selimefendigil, Fatih, Hakan F. Öztop, and Ali J. Chamkha. "MHD mixed convection of nanofluid in a cubic cavity with a conductive partition for various nanoparticle shapes." International Journal of Numerical Methods for Heat & Fluid Flow 29, no. 10 (October 7, 2019): 3584–610. http://dx.doi.org/10.1108/hff-04-2018-0176.

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Purpose This paper aims to numerically examine the mixed convection of SiO2-water nanofluid flow in a three-dimensional (3D) cubic cavity with a conductive partition considering various shapes of the particles (spherical, cylindrical, blade, brick). The purpose is to analyze the effects of various pertinent parameters such as Richardson number (between 0.1 and 10), Hartmann number (between 0 and 10), solid nanoparticle volume fraction (between 0 and 0.04), particle shape (spherical, cylindrical, blade, brick) and different heights and lengths of the conductive partition on the fluid flow and heat transfer characteristics. Design/methodology/approach The numerical simulation was performed by using Galerkin-weighted residual finite element method for various values of Richardson number, Hartmann number, solid nanoparticle volume fraction, particle shape (spherical, cylindrical, blade, brick) and different heights and lengths of the conductive partition. Two models for the average Nusselt number were proposed for nanofluids with spherical and cylindrical particle by using multi-layer feed-forward neural networks. Findings It was observed that the average Nusselt number reduces for higher values of Richardson number and Hartmann number, while enhances for higher values of nanoparticle volume fraction. Among various types of particle shapes, blade ones perform the worst and cylindrical ones perform the best in terms of heat transfer enhancement, but this is not significant which is less than 3 per cent. The average Nusselt number deteriorates by about 6.53per cent for nanofluid at the highest volume fraction of spherical particle shapes, but it is 11.75per cent for the base fluid when Hartmann number is increased from 0 to 10. Conductive partition geometrical parameters (length and height) do not contribute to much to heat transfer process for the 3D cavity, except for the case when height of the partition reaches 0.8 times the height of the cubic cavity, the average Nusselt number value reduces by about 25per cent both for base fluid and for nanofluid when compared to case with cavity height which is 0.2 times the height of the cubic cavity. Originality/value Based on the literature survey, a 3D configuration for MHD mixed convection of nanofluid flow in a cavity with a conductive partition considering the effects of various particle shapes has never been studied in the literature. This study is a first attempt to use a conductive partition with nanofluid of various particle shapes to affect the fluid flow and heat transfer characteristics in a 3D cubic cavity under the influence of magnetic field. Partial or all findings of this study could be used for the design and optimization of realistic 3D thermal configurations that are encountered in practice and some of the applications were already mentioned above. In this study, thermal performance of the system was obtained in terms of average heat transfer coefficient along the hot surface, and it is modeled with multi-layer feed-forward neural networks.

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Cha, Juhwan, and Young Kim. "Design Principles of Early Stone Pagodas in Ancient Korean Architecture: Case Studies on the Stone Pagodas at Chŏngnimsa and Kamŭnsa Buddhist Temples." Religions 10, no. 3 (March 18, 2019): 208. http://dx.doi.org/10.3390/rel10030208.

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Ancient books on East Asian mathematics introduced to the Korean Peninsula enrich our understanding of the arithmetic notions that mold the creative thought processes of the ancients. They believed that all objects in the universe could be composed of circles and squares and all items could be expressed in terms of geometrical profiles. Through the combination of circles and squares, the ancient East Asians expressed the order of the world and unraveled it mathematically. These principles are evident in the construction principles of early Korean stone pagodas. In particular, the square root of 2 (√2) is a very important number in the delineation represented in the consolidation of inscribed and circumscribed circles with squares. Further, the square root of 2 is applied as a design principle in the construction of the stone pagodas at the temples Chŏngnimsa and Kamŭnsa. This article demonstrates that the ancients on the continuous impact of the Jiuzhang Suanshu and the Zhoubi Suanshu constructed the pagodas complying with design principles based on the arithmetic and geometric proportional systems of √2 times, which are intended to adjust compositional proportions and the gradual decrease in length to shape the tripartite partition of the foundation, the pagoda body, and the finial in stone pagodas.

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Wang, Guanya, Kailiang Deng, Qi Chen, Zhiwei Li, Han Gao, Jun Hu, and Deliang Xiang. "Distributed Scatterer Processing Based on Binary Partition Trees with Multi-Baseline PolInSAR Data." Remote Sensing 14, no. 21 (October 26, 2022): 5367. http://dx.doi.org/10.3390/rs14215367.

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Distributed scatterers (DSs) are necessary to increase point density in multi-temporal InSAR (MT-InSAR) monitoring. The identification of homogeneous pixels (HPs) is the first and key step for DS processing to overcome the low signal-to-noise ratio condition. Since multi-polarization data are good at describing geometrical structures and dielectric properties of ground objects, they have been applied for HP identification. However, polarimetric information is not enough for identifying areas with similar ground objects but different deformation. We propose a novel DS preprocessing algorithm based on polarimetric interferometric homogeneous pixel (PIHP) identification. Firstly, a novel Polarimetric InSAR (PolInSAR) similarity that combines polarimetric intensity, interferometric coherence, and phase is proposed, which is readily available in multi-baseline and multi-polarization data and flexible by controlling weighting factors. Secondly, based on the binary partition tree (BPT) framework, object-orientated multi-scale PIHP identification is achieved, which is suitable for complex deformation scenes. Tested with simulated quad-polarization data, our method shows improvement in phase quality and point density, especially in the deformed areas, compared with the traditional HP identification method based on the polarimetric homogeneity (PolHom) test and the method with ground object type map. Tested with 30 quad-polarization Radarsat-2 images over Kilauea Volcano, the point density of our method is three times higher than that of the PolHom test in vegetation areas. Our method is proven to be more sensitive and mechanically more advanced to homogeneous pixels identification than the traditional ones, which is helpful for phase optimization, spatial enlargement of monitoring points, and stability of the MT-InSAR algorithm.

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Zhang, Tiehui, Jun Liu, Hengyu Li, Shaorong Xie, and Luo Jun. "Group consensus coordination control in networked nonholonomic multirobot systems." International Journal of Advanced Robotic Systems 18, no. 4 (July 1, 2021): 172988142110277. http://dx.doi.org/10.1177/17298814211027701.

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In this article, the coordination control problem of group tracking consensus is considered for networked nonholonomic mobile multirobot systems (NNMMRSs). This problem framework generalizes the findings of complete consensus in NNMMRSs and group consensus in networked Lagrangian systems (NLSs), enjoying capacious application backgrounds. By leveraging a kinematic controller embedded in the adaptive torque control protocols, a new convergence criterion of group consensus is established. In contrast to the formulation under strict algebraic assumptions, it is found that group tracking consensus for NNMMRSs can be realized under a simple geometrical condition. The system stability analysis is dictated by the property of network topology with acyclic partition. Finally, the theoretical achievements are verified by illustrative numerical examples. The results show an interesting phenomenon that, for NNMMRSs, the state responses exhibit negative correlation with the algebraic connectivity and coupling strength.

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Basili, Michela, and Anna Sinopoli. "Masonry Walls as Orthotropic No Tension Structures." Advanced Materials Research 133-134 (October 2010): 313–18. http://dx.doi.org/10.4028/www.scientific.net/amr.133-134.313.

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In this paper, following the research line proposed by Milankovicth (1910) and Signorini (1925), a semi-analytical approach for the analysis of masonry walls - treated as horizontally multi-layered strata of no-tension material - is proposed in order to evaluate the stress distribution generated by applied loads. The main applications concern walls subjected only to vertical loads. The goal is to identify in the masonry wall the actual bearing sub-structures by defining at each vertical and horizontal level the transversal sections generated by the unilateral behaviour. The method proposed will allow identifying the partition of the wall into macro-elements, which depend on the centre of applied loads, and wall and bricks geometrical features. The technique adopted to approach the problem can be referred to as the search for the best shape. Two cases are discussed: corbelled masonry walls surrounding windows and arch behaviour of masonry over the window.

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Tiňo, Peter, Bill G. Horne, and C. Lee Giles. "Attractive Periodic Sets in Discrete-Time Recurrent Networks (with Emphasis on Fixed-Point Stability and Bifurcations in Two-Neuron Networks)." Neural Computation 13, no. 6 (June 1, 2001): 1379–414. http://dx.doi.org/10.1162/08997660152002898.

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We perform a detailed fixed-point analysis of two-unit recurrent neural networks with sigmoid-shaped transfer functions. Using geometrical arguments in the space of transfer function derivatives, we partition the network state-space into distinct regions corresponding to stability types of the fixed points. Unlike in the previous studies, we do not assume any special form of connectivity pattern between the neurons, and all free parameters are allowed to vary. We also prove that when both neurons have excitatory self-connections and the mutual interaction pattern is the same (i.e., the neurons mutually inhibit or excite themselves), new attractive fixed points are created through the saddle-node bifurcation. Finally, for an N-neuron recurrent network, we give lower bounds on the rate of convergence of attractive periodic points toward the saturation values of neuron activations, as the absolute values of connection weights grow.

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Lytridis, Chris, Anna Lekova, Christos Bazinas, Michail Manios, and Vassilis G. Kaburlasos. "WINkNN: Windowed Intervals’ Number kNN Classifier for Efficient Time-Series Applications." Mathematics 8, no. 3 (March 13, 2020): 413. http://dx.doi.org/10.3390/math8030413.

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Our interest is in time series classification regarding cyber–physical systems (CPSs) with emphasis in human-robot interaction. We propose an extension of the k nearest neighbor (kNN) classifier to time-series classification using intervals’ numbers (INs). More specifically, we partition a time-series into windows of equal length and from each window data we induce a distribution which is represented by an IN. This preserves the time dimension in the representation. All-order data statistics, represented by an IN, are employed implicitly as features; moreover, parametric non-linearities are introduced in order to tune the geometrical relationship (i.e., the distance) between signals and consequently tune classification performance. In conclusion, we introduce the windowed IN kNN (WINkNN) classifier whose application is demonstrated comparatively in two benchmark datasets regarding, first, electroencephalography (EEG) signals and, second, audio signals. The results by WINkNN are superior in both problems; in addition, no ad-hoc data preprocessing is required. Potential future work is discussed.

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Guo, Sheng, Wei Ye, Haibo Qu, Dan Zhang, and Yuefa Fang. "A serial of novel four degrees of freedom parallel mechanisms with large rotational workspace." Robotica 34, no. 4 (July 9, 2014): 764–76. http://dx.doi.org/10.1017/s0263574714001842.

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SUMMARYIn this paper, a class of novel four Degrees of Freedom (DOF) non-overconstrained parallel mechanisms with large rotational workspace is presented based on screw theory. First, the conflict between the number of independent constraints applied on the moving platform and the number of kinematic limbs for 4-DOF non-overconstrained parallel mechanism is identified. To solve this conflict, the platform partition method is introduced, and two secondary platforms are employed in each of the parallel mechanisms. Then, the motion requirements of the secondary platforms are analyzed and all the possible kinematic chains are enumerated. The geometrical assembly conditions of all possible secondary limbs are analyzed and some typical non-overconstrained parallel mechanisms are generated. In each of the parallel mechanisms, a planetary gear train is used to connect both of the secondary platforms. The large rotational workspace of the moving platform is obtained due to the relative motion of the two secondary platforms. Finally, the kinematics analysis of a typical parallel mechanism is conducted.

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Gajjar, Margi, and Himanshu Pathak. "Fracture analysis of plastically graded material with thermo-mechanical J-integral." Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications 235, no. 5 (February 3, 2021): 1128–45. http://dx.doi.org/10.1177/1464420721991583.

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In this paper, the influence of plasticity graded property and thermal boundary conditions have been investigated on the fracture parameter, i.e. J-integral using the extended finite element method. A complete computational methodology has been presented to model elasto-plastic fracture problems with geometrical and material nonlinearities. For crack discontinuity modeling, a partition of unity enrichment concept was employed with additional mathematical functions like Heaviside and branch enrichment for crack discontinuity and stress field gradient, respectively. The modeling of the stress–strain relationship of the material is implemented using the Ramberg–Osgood material model and geometric nonlinearity is modeled using an updated Lagrangian approach. The isotropic hardening and von-Mises yield criteria are considered to check the plasticity condition. The elastic predictor–plastic corrector algorithm is employed to capture elasto-plastic stress in a cracked domain. The variation in plasticity properties for plastically graded material is modeled by exponential law. Furthermore, the nonlinear discrete equations are numerically solved using a Newton–Raphson iterative scheme. Various cracked problem geometries subjected to thermal (adiabatic and isothermal conditions) and thermo-mechanical loads are simulated for stress contours and J-integrals using the elasto-plastic fracture mechanics approach. A comparison of the results obtained using extended finite element method with literature and the finite element analysis (FEA) package shows the accuracy and effectiveness of the presented computational approach. A component-based problem, i.e. a Brazilian disc subjected to thermo-mechanical loading, has been solved to show the adaptability of this work.

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Formetta, G., R. Mantilla, S. Franceschi, A. Antonello, and R. Rigon. "The JGrass-NewAge system for forecasting and managing the hydrological budgets at the basin scale: the models of flow generation, propagation, and aggregation." Geoscientific Model Development Discussions 4, no. 2 (April 29, 2011): 943–69. http://dx.doi.org/10.5194/gmdd-4-943-2011.

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Abstract. This paper presents a discussion of the predictive capacity of the first implementation of the semi-distributed hydrological modeling system JGrass-NewAge. This model focuses on the hydrological balance of medium scale to large scale basins, and considers statistics of the processes at the hillslope scale. The whole modeling system consists of six main parts: (i) estimation of energy balance; (ii) estimation of evapotranspiration; (iii) snow modelling; (iv) estimation of runoff production; (v) aggregation and propagation of flows in channel, and (vi) description of intakes, out-takes, and reservoirs. This paper details the processes, of runoff production, and aggregation/propagation of flows on a river network. The system is based on a hillslope-link geometrical partition of the landscape, so the basic unit, where the budget is evaluated, consists of hillslopes that drain into a single associated link rather than cells or pixels. To this conceptual partition corresponds an implementation of informatics that uses vectorial features for channels, and raster data for hillslopes. Runoff production at each channel link is estimated through a combination of the Duffy (1996) model and a GIUH model for estimating residence times in hillslope. Routing in channels uses equations integrated for any channels' link, and produces discharges at any link end, for any link in the river network. The model has been tested against measured discharges according to some indexes of goodness of fit such as RMSE and Nash Sutcliffe. The characteristic ability to reproduce discharge in any point of the river network is used to infer some statistics, and notably, the scaling properties of the modeled discharge.

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PERFECT, E., A. M. TARQUIS, and N. R. A. BIRD. "ACCURACY OF GENERALIZED DIMENSIONS ESTIMATED FROM GRAYSCALE IMAGES USING THE METHOD OF MOMENTS." Fractals 17, no. 03 (September 2009): 351–63. http://dx.doi.org/10.1142/s0218348x09004302.

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The moment-based box counting method of multifractal analysis is widely used for estimating generalized dimensions, Dq, from two-dimensional grayscale images. An evaluation of the accuracy of this method is needed to establish confidence in the resulting estimates of Dq. We estimated Dq from q = -10 to +10 for 23 random geometrical multifractal fields with different grid sizes, and known analytical Dq versus q functions. The fields were transformed to give normalized grayscale values between zero and one. Comparison of the estimated and analytical functions indicated the moment-based box counting method overestimates Dq by as much as 6.9% when q ≪ 0. The root mean square error, RMSE, for the entire range of q values examined ranged from 7.81 × 10-6 to 1.35 × 10-1, with a geometric mean of 6.50 × 10-3. The RMSE decreased with decreasing grid size and increasing heterogeneity. These trends appear to be largely due to the presence of zeros in the normalized grayscale fields. Variations in the slope of the log-transformed partition function, ln [χ(q,δ)], with box size resulted in the overestimation of Dq when q ≪ 0. An alternative procedure for estimating Dq was developed based on the numerical first derivatives of ln [χ(q,δ)]. Using this approach the maximum deviation in Dq values was only 1.2%, while the RMSE varied from 3.11 × 10-6 to 2.72 × 10-2, with a geometric mean of 2.57 × 10-4. When analyzing normalized grayscale fields, moment-based estimates of Dq should be interpreted with care. An order of magnitude increase in the accuracy of Dq can be achieved for such fields if the numerical first derivatives of ln [χ(q,δ)] are used in the analysis instead of standard linear regression.

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Merciol, F., M. T. Pham, D. Santana Maia, A. Masse, and C. Sannier. "BROCELIANDE: A COMPARATIVE STUDY OF ATTRIBUTE PROFILES AND FEATURE PROFILES FROM DIFFERENT ATTRIBUTES." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLIII-B3-2020 (August 22, 2020): 1371–77. http://dx.doi.org/10.5194/isprs-archives-xliii-b3-2020-1371-2020.

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Abstract. Morphological attribute profiles (APs) are among the most effective spatial-spectral methods to perform multilevel image description based on hierarchical tree-based representation. They have been widely applied to the processing and characterization of remote sensing images, in particular to tackle classification task, in the literature. Recently, a novel extension of APs called FPs has been proposed by replacing pixel gray-levels with some statistical and geometrical features when forming the output profiles. FPs have been proved to be more efficient than the standard APs when generated from both inclusion and partition trees. The motivation of this article is to conduct a comparative study of APs and FPs using different attributes including some novel ones that have not been used in the literature. We also present our developed library called Broceliande, which proposes efficient implementation of APs and FPs to perform remote sensing image classification, with various choices of tree structures as well as attributes. We perform our experiments on two high resolution optical image data sets and provide comparative results of APs and FPs, showing and confirming their effectiveness to describe and classify remote sensing images.

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CHEN, L., G. R. LIU, and K. Y. ZENG. "A COMBINED EXTENDED AND EDGE-BASED SMOOTHED FINITE ELEMENT METHOD (ES-XFEM) FOR FRACTURE ANALYSIS OF 2D ELASTICITY." International Journal of Computational Methods 08, no. 04 (November 20, 2011): 773–86. http://dx.doi.org/10.1142/s0219876211002812.

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This study combines the edge-based smoothed finite element method (ES-FEM) and the extended finite element method (XFEM) to develop a new simulation technique (ES-XFEM) for fracture analysis of 2D elasticity. In the XFEM, the need for the mesh alignment with the crack and remeshing, as the crack evolves, is eliminated because of the use of partition of unity. The ES-FEM uses the generalized smoothing operation over smoothing domain associated with edges of simplex meshes, and produces a softening effect leading to a close-to-exact stiffness, "super-convergence" and "ultra-accurate" solutions for the numerical model. Taking advantage of both ES-FEM and XFEM, the present method introduces the edge-based strain smoothing technique into the context of XFEM. Thanks to strain smoothing, the necessity of sub-division in elements cut by discontinuities is suppressed via transforming interior integration into boundary integration. Hence, it simplifies the numerical integration procedure in the XFEM. Numerical examples showed that the proposed method improves significantly the accuracy of stress intensity factors and achieves a quasi optimal convergence rate in the energy norm without geometrical enrichment or blending correction.

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ZHOU, H., E. PERFECT, B. G. LI, and Y. Z. LU. "EFFECTS OF BIT DEPTH ON THE MULTIFRACTAL ANALYSIS OF GRAYSCALE IMAGES." Fractals 18, no. 01 (March 2010): 127–38. http://dx.doi.org/10.1142/s0218348x10004749.

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Multifractal box counting analysis has been widely applied to study the scaling characteristics of grayscale images. Since bit depth is an important property of such images it is desirable know the impact of varying bit depths on the estimation of the generalized dimensions (Dq). We generated random geometrical multifractal grayscale fields, which were then transformed from double precision to 16, 13, and 8 bit depths. Digitized grayscale images of soil thin sections at 13 bit depth were also selected for study and transformed to 8 bit depth. The moment based box counting method was applied to evaluate the bit depth effects on Dq. The partition functions for the multifractal fields became noticeably nonlinear on a log-log scale when q ≪ 0 as the bit depth decreased. This trend can be attributed to loss of grayscale details, changes in the local mass distribution, and the occurrence of zeros due to the bit depth transformation and data normalization processes. These effects were most pronounced for positively skewed multifractal fields, with a high proportion of extremely small mass fractions. As a result, the generalized dimensions estimated by linear regression were not always accurate, and an alternative method based on numerical derivatives was explored. The numerical method significantly improved the accuracy of the multifractal analyses; the maximum absolute difference between the analytical and numerically-derived estimates of Dq was only 9.62 × 10-3. However, when applied to situations in which the box counting scale factor did not match the scale factor used to generate the multifractal field, the numerically-derived estimates of Dq were severely biased. In this case, the linear regression method is preferable even though some error may occur due to limited bit depths. All of the soil grayscale images exhibited multifractal scaling characteristics, although there was little effect of bit depth on the resulting Dq values. Because of random fluctuations in the partition functions, the linear regression method proved to be more robust than the numerical derivative method for estimating the generalized dimensions of natural grayscale images.

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Moraglio, Alberto, Yong-Hyuk Kim, Yourim Yoon, and Byung-Ro Moon. "Geometric Crossovers for Multiway Graph Partitioning." Evolutionary Computation 15, no. 4 (December 2007): 445–74. http://dx.doi.org/10.1162/evco.2007.15.4.445.

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Geometric crossover is a representation-independent generalization of the traditional crossover defined using the distance of the solution space. By choosing a distance firmly rooted in the syntax of the solution representation as a basis for geometric crossover, one can design new crossovers for any representation. Using a distance tailored to the problem at hand, the formal definition of geometric crossover allows us to design new problem-specific crossovers that embed problem-knowledge in the search. The standard encoding for multiway graph partitioning is highly redundant: each solution has a number of representations, one for each way of labeling the represented partition. Traditional crossover does not perform well on redundant encodings. We propose a new geometric crossover for graph partitioning based on a labeling-independent distance that filters out the redundancy of the encoding. A correlation analysis of the fitness landscape based on this distance shows that it is well suited to graph partitioning. A second difficulty with designing a crossover for multiway graph partitioning is that of feasibility: in general recombining feasible partitions does not lead to feasible offspring partitions. We design a new geometric crossover for permutations with repetitions that naturally suits partition problems and we test it on the graph partitioning problem. We then combine it with the labeling-independent crossover and obtain a much superior geometric crossover inheriting both advantages.

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Shen, Yiou, Bing Jiang, and Yan Li. "Scale Effect on Impact Performance of Unidirectional Glass Fiber Reinforced Epoxy Composite Laminates." Materials 12, no. 8 (April 23, 2019): 1319. http://dx.doi.org/10.3390/ma12081319.

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As a result of the increasing use of glass fiber reinforced plastic (GFRP) composites in engineering fields, the investigation of scale effect on impact performance for this kind of composite is essential for large scale structure design. The effects of scaling on the impact response of simply supported unidirectional GFRP were investigated through drop weight impact (DWI) tests in this study. Impact tests were undertaken over a wide range of energies to generate damages between barely visible and initiated penetration on four scale size GFRP laminates. The main impact responses including impact force, contact duration, displacement, energy absorption and damage area of scaled specimens were normalized to compare with the full-size specimen. It was found that the impact response of large sample with elastic deformation and small area of delamination can be predicted accurately according to a geometrical similar scaling law. Scale effect was found in the damage threshold force and absorbed energy of the laminates when significant internal damage occurs due to the microstructural effect becoming important in resisting impact force and absorbing impact energy. Moreover, the energy partition and effective stiffness were calculated according to the energy balance model to reveal the contribution of different modes of deformations on energy absorption for the GFRP laminates.

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Wang, Jing, Jingchi Yang, Fengling Yang, and Fangqin Cheng. "Numerical and Experimental Investigation of the Decoupling Combustion Characteristics of a Burner with Flame Stabilizer." Energies 16, no. 11 (June 1, 2023): 4474. http://dx.doi.org/10.3390/en16114474.

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In order to integrate renewable electricity into the power grid, it is crucial for coal-fired power plant boilers to operate stably across a wide load range. Achieving steady combustion with low nitrogen oxide (NOx) emissions poses a significant challenge for boilers burning low-volatile coal in coal-fired power plants. This study focuses on developing a decoupling combustion technology for low-volatile coal-fired boilers operating at low loads. A three-dimensional numerical simulation is employed to analyze and optimize the geometrical parameters of a burner applied in a real 300 MW pulverized coal fired boiler. Detailed analysis of the burner’s decoupling combustion characteristics, including stable combustion ability and NOx reduction principles, is conducted. The results indicate that this burner showed three stages of coal/air separation, and the flame holder facilitates the stepwise spontaneous ignition and combustion of low-volatile coal. By extending the time between coal pyrolysis and carbon combustion, the burner enhances decoupling combustion and achieves low nitrogen oxide emissions. Based on optimization, a flat partition plate without inclination demonstrates excellent performance in terms of velocity vector field distribution, coal air flow rich/lean separation, combustion, and nitrogen oxide generation. Compared with the initial structural design, the average nitrogen oxide concentration at the outlet is reduced by 59%.

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DAVISON, BEN, JARED ONGARO, and BALÁZS SZENDRŐI. "Enumerating coloured partitions in 2 and 3 dimensions." Mathematical Proceedings of the Cambridge Philosophical Society 169, no. 3 (July 19, 2019): 479–505. http://dx.doi.org/10.1017/s0305004119000252.

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AbstractWe study generating functions of ordinary and plane partitions coloured by the action of a finite subgroup of the corresponding special linear group. After reviewing known results for the case of ordinary partitions, we formulate a conjecture concerning a basic factorisation property of the generating function of coloured plane partitions that can be thought of as an orbifold analogue of a conjecture of Maulik et al., now a theorem, in three-dimensional Donaldson–Thomas theory. We study natural quantisations of the generating functions arising from geometry, discuss a quantised version of our conjecture, and prove a positivity result for the quantised coloured plane partition function under a geometric assumption.

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Journal articles on the topic 'Geometrical Partition'

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