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1
Buczolich. "ANOTHER NOTE ON THE GRADIENT PROBLEM OF C. E. WEIL." Real Analysis Exchange 22, no. 2 (1996): 775. http://dx.doi.org/10.2307/44153954.
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Buczolich. "PROGRESS MADE RELATED TO THE GRADIENT PROBLEM OF C. E. WEIL." Real Analysis Exchange 22, no. 1 (1996): 79. http://dx.doi.org/10.2307/44152725.
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Liebold, Christian, and Wolfgang H. Müller. "1D HERMITE ELEMENTS FOR C1-CONTINUOUS SOLUTIONS IN SECOND GRADIENT ELASTICITY." Acta Polytechnica CTU Proceedings 7 (December 9, 2016): 33–37. http://dx.doi.org/10.14311/app.2017.7.0033.
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We present a modified strain gradient theory of elasticity for linear isotropic materials in order to account for the so-called size effect. Additional material length scale parameters are introduced and the problem of static beam bending is analyzed. A numerical solution is derived by means of a finite element approach. A global C1-continuous displacement field is applied in finite element solutions because the higher-order strain energy density additionally depends on second gradients of displacements. So-called Hermite finite elements are used that allow for merging gradients between elements. The element stiffness matrix as well as the global stiffness matrix of the problem is developed. Convergence, C1-continuity and the size effect in the numerical solution is shown. Experiments on bending stiffnesses of different sized micro beams made of the polymer SU-8 are performed by using an atomic force microscope and the results are compared to the numerical solution.
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Kateb, K. M., K. H. Almitani, K. A. Alnefaie, N. H. Abu-Hamdeh, P. Papadopoulos, H. Askes, and E. C. Aifantis. "Application of gradient elasticity to benchmark problems of beam vibrations." Journal of the Mechanical Behavior of Materials 25, no. 1-2 (April 1, 2016): 33–51. http://dx.doi.org/10.1515/jmbm-2016-0001.
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AbstractThe gradient approach, specifically gradient elasticity theory, is adopted to revisit certain typical configurations on mechanical vibrations. New results on size effects and scale-dependent behavior not captured by classical elasticity are derived, aiming at illustrating the usefulness of this approach to applications in advanced technologies. In particular, elastic prismatic straight beams in bending are discussed using two different governing equations: the gradient elasticity bending moment equation (fourth order) and the gradient elasticity deflection equation (sixth order). Different boundary/support conditions are examined. One problem considers the free vibrations of a cantilever beam loaded by an end force. A second problem is concerned with a simply supported beam disturbed by a concentrated force in the middle of the beam. Both problems are solved analytically. Exact free vibration frequencies and mode shapes are derived and presented. The difference between the gradient elasticity solution and its classical counterpart is revealed. The size ratio c/L (c denotes internal length and L is the length of the beam) induces significant effects on vibration frequencies. For both beam configurations, it turns out that as the ratio c/L increases, the vibration frequencies decrease, a fact which implies lower beam stiffness. Numerical examples show this behavior explicitly and recover the classical vibration behavior for vanishing size ratio c/L.
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Sirirut, Taksaporn, and Pattanapong Tianchai. "On Solving of Constrained Convex Minimize Problem Using Gradient Projection Method." International Journal of Mathematics and Mathematical Sciences 2018 (October 1, 2018): 1–10. http://dx.doi.org/10.1155/2018/1580837.
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Let C and Q be closed convex subsets of real Hilbert spaces H1 and H2, respectively, and let g:C→R be a strictly real-valued convex function such that the gradient ∇g is an 1/L-ism with a constant L>0. In this paper, we introduce an iterative scheme using the gradient projection method, based on Mann’s type approximation scheme for solving the constrained convex minimization problem (CCMP), that is, to find a minimizer q∈C of the function g over set C. As an application, it has been shown that the problem (CCMP) reduces to the split feasibility problem (SFP) which is to find q∈C such that Aq∈Q where A:H1→H2 is a linear bounded operator. We suggest and analyze this iterative scheme under some appropriate conditions imposed on the parameters such that another strong convergence theorems for the CCMP and the SFP are obtained. The results presented in this paper improve and extend the main results of Tian and Zhang (2017) and many others. The data availability for the proposed SFP is shown and the example of this problem is also shown through numerical results.
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Jerrard, Robert L., Amir Moradifam, and Adrian I. Nachman. "Existence and uniqueness of minimizers of general least gradient problems." Journal für die reine und angewandte Mathematik (Crelles Journal) 2018, no. 734 (January 1, 2018): 71–97. http://dx.doi.org/10.1515/crelle-2014-0151.
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AbstractMotivated by problems arising in conductivity imaging, we prove existence, uniqueness, and comparison theorems – under certain sharp conditions – for minimizers of the general least gradient problem\inf_{u\in BV_{f}(\Omega)}\int_{\Omega}\varphi(x,Du), wheref:\partial\Omega\to\mathbb{R}is continuous,BV_{f}(\Omega):=\bigl{\{}v\in BV(\Omega):\lim_{r\to 0}\operatornamewithlimits{% ess\,sup}_{y\in\Omega,|x-y|<r}|f(x)-v(y)|=0\text{ for }x\in\partial\Omega\bigr% {\}}and\varphi(x,\xi)is a function that, among other properties, is convex and homogeneous of degree 1 with respect to the ξ variable. In particular, we prove that ifa\in C^{1,1}(\Omega)is bounded away from zero, then minimizers of the weighted least gradient problem\inf_{u\in BV_{f}}\int_{\Omega}a|Du|are unique inBV_{f}(\Omega). We construct counterexamples to show that the regularity assumptiona\in C^{1,1}is sharp, in the sense that it can not be replaced bya\in C^{1,\alpha}(\Omega)with any\alpha<1.
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Kumarasamy, Sakthivel, and Alemdar Hasanov. "An inverse problem for the KdV equation with Neumann boundary measured data." Journal of Inverse and Ill-posed Problems 26, no. 1 (February 1, 2018): 133–51. http://dx.doi.org/10.1515/jiip-2017-0038.
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AbstractIn this paper, we consider an inverse coefficient problem for the linearized Korteweg–de Vries (KdV) equation {u_{t}+u_{xxx}+(c(x)u)_{x}=0}, with homogeneous boundary conditions {u(0,t)=u(1,t)=u_{x}(1,t)=0}, when the Neumann data{g(t):=u_{x}(0,t)}, {t\in(0,T)}, is given as an available measured output at the boundary {x=0}. The inverse problem is formulated as a minimum problem for the regularized Tikhonov functional {\mathcal{J}_{\alpha}(c)=\frac{1}{2}\|u_{x}(0,\cdot\,;c)-g\|^{2}_{L^{2}(0,T)}+% \frac{\alpha}{2}\|c^{\prime}\|^{2}_{L^{2}(0,1)}} with Sobolev norm. Based on a priori estimates for the weak and regular weak solutions of the direct and adjoint problems, it is proved that the input-output operator is compact, which shows the ill-posedness of the inverse problem. Then Fréchet differentiability of the Tikhonov functional and Lipschitz continuity of the Fréchet gradient are proved. It is shown that the last result allows us to use an important advantage of gradient methods when the functional is from the class {C^{1,1}(\mathcal{M})}. In the final part, an existence of a solution of the minimum problem for the regularized Tikhonov functional {\mathcal{J}_{\alpha}(c)} is proved.
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Chen, Jinzuo, Mihai Postolache, and Yonghong Yao. "S-Subgradient Projection Methods with S-Subdifferential Functions for Nonconvex Split Feasibility Problems." Symmetry 11, no. 12 (December 14, 2019): 1517. http://dx.doi.org/10.3390/sym11121517.
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In this paper, the original C Q algorithm, the relaxed C Q algorithm, the gradient projection method ( G P M ) algorithm, and the subgradient projection method ( S P M ) algorithm for the convex split feasibility problem are reviewed, and a renewed S P M algorithm with S-subdifferential functions to solve nonconvex split feasibility problems in finite dimensional spaces is suggested. The weak convergence theorem is established.
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Sun, Siyuan, Changchun Yin, and Xiuhe Gao. "3D Gravity Inversion on Unstructured Grids." Applied Sciences 11, no. 2 (January 13, 2021): 722. http://dx.doi.org/10.3390/app11020722.
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Compared with structured grids, unstructured grids are more flexible to model arbitrarily shaped structures. However, based on unstructured grids, gravity inversion results would be discontinuous and hollow because of cell volume and depth variations. To solve this problem, we first analyzed the gradient of objective function in gradient-based inversion methods, and a new gradient scheme of objective function is developed, which is a derivative with respect to weighted model parameters. The new gradient scheme can more effectively solve the problem with lacking depth resolution than the traditional inversions, and the improvement is not affected by the regularization parameters. Besides, an improved fuzzy c-means clustering combined with spatial constraints is developed to measure property distribution of inverted models in both spatial domain and parameter domain simultaneously. The new inversion method can yield a more internal continuous model, as it encourages cells and their adjacent cells to tend to the same property value. At last, the smooth constraint inversion, the focusing inversion, and the improved fuzzy c-means clustering inversion on unstructured grids are tested on synthetic and measured gravity data to compare and demonstrate the algorithms proposed in this paper.
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Tian, Ming, and Li-Hua Huang. "A General Approximation Method for a Kind of Convex Optimization Problems in Hilbert Spaces." Journal of Applied Mathematics 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/156073.
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The constrained convex minimization problem is to find a pointx∗with the property thatx∗∈C, andh(x∗)=min h(x),∀x∈C, whereCis a nonempty, closed, and convex subset of a real Hilbert spaceH,h(x)is a real-valued convex function, andh(x)is not Fréchet differentiable, but lower semicontinuous. In this paper, we discuss an iterative algorithm which is different from traditional gradient-projection algorithms. We firstly construct a bifunctionF1(x,y)defined asF1(x,y)=h(y)−h(x). And we ensure the equilibrium problem forF1(x,y)equivalent to the above optimization problem. Then we use iterative methods for equilibrium problems to study the above optimization problem. Based on Jung’s method (2011), we propose a general approximation method and prove the strong convergence of our algorithm to a solution of the above optimization problem. In addition, we apply the proposed iterative algorithm for finding a solution of the split feasibility problem and establish the strong convergence theorem. The results of this paper extend and improve some existing results.
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Hasanov, Alemdar. "Lipschitz continuity of the Fréchet gradient in an inverse coefficient problem for a parabolic equation with Dirichlet measured output." Journal of Inverse and Ill-posed Problems 26, no. 3 (June 1, 2018): 349–68. http://dx.doi.org/10.1515/jiip-2017-0106.
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AbstractThis paper studies the Lipschitz continuity of the Fréchet gradient of the Tikhonov functional {J(k):=(1/2)\lVert u(0,\cdot\,;k)-f\rVert^{2}_{L^{2}(0,T)}} corresponding to an inverse coefficient problem for the {1D} parabolic equation {u_{t}=(k(x)u_{x})_{x}} with the Neumann boundary conditions {-k(0)u_{x}(0,t)=g(t)} and {u_{x}(l,t)=0}. In addition, compactness and Lipschitz continuity of the input-output operator\Phi[k]:=u(x,t;k)\lvert_{x=0^{+}},\quad\Phi[\,\cdot\,]:\mathcal{K}\subset H^{1% }(0,l)\mapsto H^{1}(0,T),as well as solvability of the regularized inverse problem and the Lipschitz continuity of the Fréchet gradient of the Tikhonov functional are proved. Furthermore, relationships between the sufficient conditions for the Lipschitz continuity of the Fréchet gradient and the regularity of the weak solution of the direct problem as well as the measured output {f(t):=u(0,t;k)} are established. One of the derived lemmas also introduces a useful application of the Lipschitz continuity of the Fréchet gradient. This lemma shows that an important advantage of gradient methods comes when dealing with the functionals of class {C^{1,1}(\mathcal{K})}. Specifically, this lemma asserts that if {J\in C^{1,1}(\mathcal{K})} and {\{k^{(n)}\}\subset\mathcal{K}} is the sequence of iterations obtained by the Landweber iteration algorithm {k^{(n+1)}=k^{(n)}+\omega_{n}J^{\prime}(k^{(n)})}, then for {\omega_{n}\in(0,2/L_{g})}, where {L_{g}>0} is the Lipschitz constant, the sequence {\{J(k^{(n)})\}} is monotonically decreasing and {\lim_{n\to\infty}\lVert J^{\prime}(k^{(n)})\rVert=0}.
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Jin, Qi, Xue Ping Ren, Hong Liang Hou, Yan Ling Zhang, and Hai Tao Qu. "In Situ Synthesis and Structural Design of Ti/TiC Functionally Graded Materials." Materials Science Forum 913 (February 2018): 515–21. http://dx.doi.org/10.4028/www.scientific.net/msf.913.515.
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In this paper, the metal/ceramic functionally graded composites are prepared. The thermal stress of TiC/Ti functionally graded composites are simulated by Abaqus finite element analysis software to study the influence of the number of layers, the gradient layer thickness and the gradient of distribution index.The optimal structural parameters of the TiC/Ti functional gradient composites are obtained as the number of layers of 6 and the gradient distribution index 0.8. According to the optimized structural parameters, Ti and C powders are mixed by high-energy ball milling, then the TiC/Ti functional gradient composites are prepared by spark plasma sintering. The gradient distribution of composition and microstructure in TiC/Ti functionally graded composites are achieved, which can solve the problem of mismatch for the physical properties between the metal and the ceramic in the composite material.
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Chaouai, Zakariya, and Soufiane Maatouk. "Multiplicity of Solutions for a Class of Elliptic Problem of p-Laplacian Type with a p-Gradient Term." International Journal of Mathematics and Mathematical Sciences 2019 (February 5, 2019): 1–10. http://dx.doi.org/10.1155/2019/6824502.
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We consider the following problem: -Δpu=c(x)|u|q-1u+μ|∇u|p+h(x) in Ω, u=0 on ∂Ω, where Ω is a bounded set in RN (N≥3) with a smooth boundary, 1<p<N, q>0, μ∈R⁎, and c and h belong to Lk(Ω) for some k>N/p. In this paper, we assume that c≩0 a.e. in Ω and h without sign condition and then we prove the existence of at least two bounded solutions under the condition that ck and hk are suitably small. For this purpose, we use the Mountain Pass theorem, on an equivalent problem to (P) with variational structure. Here, the main difficulty is that the nonlinearity term considered does not satisfy Ambrosetti and Rabinowitz condition. The key idea is to replace the former condition by the nonquadraticity condition at infinity.
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Milyukova, Olga Yurievna. "MPI+OpenMP parallel implementation of conjugate gradient method with preconditioner of block partial inverse triangular decomposition of IC2S and IC1." Keldysh Institute Preprints, no. 48 (2021): 1–32. http://dx.doi.org/10.20948/prepr-2021-48.
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The paper proposes a new preconditioner for solving systems of linear algebraic equations with a symmetric positively defined matrix by the method of conjugate gradients – Block Incomplete Inverse Cholesky BIIC preconditioner in combination with a triangular first-order decomposition "by value" - BIIC-IC1. The algorithm based on MPI+OpenMP techniques is proposed for the construction and application of the BIIC preconditioner combined with stabilized triangular decomposition of the second order "by value" (BIIC-IS2S). In this case, the BIIC-IC2S preconditioner uses the number of blocks multiple of the number of processors used and the number of threads used. Two algorithms based on MPI+OpenMP techniques are proposed for the construction and application of the BIIC-IC1 preconditioner. Comparative timing results for the MPI+OpenMP and MPI implementations of the proposed preconditioning used with the conjugate gradient method for a model problem and the sparse matrix collections SuiteSparse are presented.
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FU, X. R., W. HORTON, I. O. BESPAMYATNOV, W. L. ROWAN, S. BENKADDA, C. L. FIORE, S. FUTATANI, and K. T. LIAO. "Turbulent impurity transport modeling for Alcator C-Mod." Journal of Plasma Physics 79, no. 5 (June 3, 2013): 837–46. http://dx.doi.org/10.1017/s0022377813000548.
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AbstractTurbulent particle transport is investigated with a quasilinear theory that is motivated by the boron impurity transport experiments in the Alcator C-Mod. Eigenvalue problems for sets of reduced fluid equations for multi-component plasmas are solved for the self-consistent fluctuating field vectors composed of the electric potential φ, the main ion density δni, the impurity density δnz and the ion temperature fluctuation δTi. For Alcator C-Mod parameters, we investigate two drift wave models: (1) the density-gradient-driven impurity drift wave and (2) the ion-temperature-gradient-driven ion temperature gradient (ITG) mode. Analytic and numerical results for particle transport coefficients are derived and compared with the transport data and the neoclassical theory. We explore the ability of the model to explain impurity density profiles in three confinement regimes: H-mode, I-mode and internal transport barrier (ITB) regime in C-Mod. Related experiments reported on the Large Helical Device are briefly discussed.
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Krasnoshchok, Mykola. "Optimal control problem for an equation of filtration with memory." Proceedings of the Institute of Applied Mathematics and Mechanics NAS of Ukraine 33 (December 27, 2019): 142–57. http://dx.doi.org/10.37069/1683-4720-2019-33-12.
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Fractional diffusion models are generalization to the diffusion models with integer derivatives. There has been great interest in the study of this models because of their appearance in modeling various applications in the physical sciences, medicine and biology. We consider a filtration model with nonclassical Darcy's constitutive equation. Resulting equation states that the flux of fluid is proportional to not only gradient pressure but it's Riemann-Liouville fractional derivative also. This model was proposed by M. Caputo and allows the permeability varies with time depending on the previous pressure gradient. These phenomena, which we will represent mathematically with memory formalisms, have often been observed qualitatively in oil extraction, in geothermal areas and in the laboratory Similar problems arises in the study of flow of generalized second grade fluid. Existence results of initial and boundary value problems for partial fractional differential equations have been studied by E. Bazhlekova, K. Diethelm, J. Janno, A.N. Kochubei, G.P. Lopushans'ka, R. Zacher and others. Fractional optimal control problems have attracted for example R.Dorville, G.M. Mophou, V.S. Valmo\-rin, Y. Zhou, L. Peng and many techniques have been developed for solving such problems. We consider the problem of minimization of the standard cost functional $J(u)$ which is determined in the terms of generalized solution of initial-boundary problem of time-fractional differential equation under considerations. We consider a control via right hand term $u$ and an observation on the whole domain in $L_2$ norm with a Tikhonov regularizer term. First we introduce functional spaces and establish some auxiliary properties of fractional integrals and fractional derivatives. Second we prove an existence and uniqueness result for the state problem. We remind that we deals with an equation of filtration with memory. Our objectives are: a) to prove that there exists a minimizer $u$ of the cost functional $J$; b) to obtain necessary and sufficient conditions for $u$ to be an extremum; c) to obtain constructive algorithm amenable to computations for approximations of the optimal control. An unique solvability of state and conjugate problem is established by the help of Galerkin method and corresponding a priori estimates. Then we prove that the cost functional is coercive, convex and weakly lower semicontinuous. We show the existence of the optimal solution by proving the existence of the weakly convergent minimization sequence satisfying the state equation. The uniqueness follows directly from the strong convexity of the cost functional. This gives us the item a). The item b) is obtained from the first order optimality condition. We justify also the conjugated gradient method to search the optimal control function. On this way we use some results of R. Winther, which allows us to use the conjugate gradient method in our situation and prove its superlinear convergence.
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Chen, Wei, Weizhong Zhang, and Haoyu Zhao. "Gradient Method for Continuous Influence Maximization with Budget-Saving Considerations." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 01 (April 3, 2020): 43–50. http://dx.doi.org/10.1609/aaai.v34i01.5332.
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Continuous influence maximization (CIM) generalizes the original influence maximization by incorporating general marketing strategies: a marketing strategy mix is a vector x = (x1, …, xd) such that for each node v in a social network, v could be activated as a seed of diffusion with probability hv(x), where hv is a strategy activation function satisfying DR-submodularity. CIM is the task of selecting a strategy mix x with constraint ∑ixi ≤ k where k is a budget constraint, such that the total number of activated nodes after the diffusion process, called influence spread and denoted as g(x), is maximized. In this paper, we extend CIM to consider budget saving, that is, each strategy mix x has a cost c(x) where c is a convex cost function, and we want to maximize the balanced sum g(x) + λ(k − c(x)) where λ is a balance parameter, subject to the constraint of c(x) ≤ k. We denote this problem as CIM-BS. The objective function of CIM-BS is neither monotone, nor DR-submodular or concave, and thus neither the greedy algorithm nor the standard result on gradient method could be directly applied. Our key innovation is the combination of the gradient method with reverse influence sampling to design algorithms that solve CIM-BS: For the general case, we give an algorithm that achieves (½ − ε)-approximation, and for the case of independent strategy activations, we present an algorithm that achieves (1 − 1/e − ε) approximation.
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Yu, Peng, Ruiqing Li, Dapeng Bie, Xiancai Liu, Xiaomin Yao, and Yahui Duan. "Precise Simulation of Heat-Flow Coupling of Pipe Cooling in Mass Concrete." Materials 14, no. 18 (September 8, 2021): 5142. http://dx.doi.org/10.3390/ma14185142.
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For a long time, temperature control and crack prevention of mass concrete is a difficult job in engineering. For temperature control and crack prevention, the most effective and common-used method is to embed cooling pipe in mass concrete. At present, there still exists some challenges in the precise simulation of pipe cooling in mass concrete, which is a complex heat-flow coupling problem. Numerical simulation is faced with the problem of over-simplification and inaccuracy. In this study, precise simulation of heat-flow coupling of pipe cooling in mass concrete is carried out based on finite element software COMSOL Multiphysics 5.4. Simulation results are comprehensively verified with results from theoretical solutions and equivalent algorithms, which prove the correctness and feasibility of precise simulation. Compared with an equivalent algorithm, precise simulation of pipe cooling in mass concrete can characterize the sharp temperature gradient around cooling pipe and the temperature rise of cooling water along pipeline more realistically. In addition, the cooling effects and local temperature gradient under different water flow (0.60 m3/h, 1.20 m3/h, and 1.80 m3/h) and water temperature (5 °C, 10 °C, and 15 °C) are comprehensively studied and related engineering suggestions are given.
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Ma, Zhaoyang, Yunwei Xu, Shu Li, Qingda Yang, Xingming Guo, and Xianyue Su. "A Conforming A-FEM for Modeling Arbitrary Crack Propagation and Branching in Solids." International Journal of Applied Mechanics 13, no. 01 (January 2021): 2150010. http://dx.doi.org/10.1142/s1758825121500101.
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In this paper, an improved conforming AFEM (C-AFEM) for efficient modeling of arbitrary crack propagation and branching is proposed and validated. An explicit formulation for branching cracks has been derived within the C-AFEM framework. The conjugate gradient method is integrated into the C-AFEM formulation to solve the local problem that consists of all elements traversed by single or multiple cracks. Multiple numerical evidences show that this new approach can substantially improve the modeling efficiency. The solution accuracy and numerical robustness are also significantly improved.
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MARCHYLO, B. A. "BARLEY CULTIVAR IDENTIFICATION BY SDS GRADIENT PAGE ANALYSIS OF HORDEIN." Canadian Journal of Plant Science 67, no. 4 (October 1, 1987): 927–44. http://dx.doi.org/10.4141/cjps87-131.
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Sodium dodecyl sulfate gradient polyacrylamide gel electrophoresis (SDSGPAGE) was evaluated to determine whether it could provide improved resolving power of hordein proteins concomitant with improved discrimination (identification) of Canadian barley cultivars. Hordeins were subjected to electrophoresis using a linear gradient gel and a discontinuous buffer system. Proteins were detected using a silver-based color stain and gels were calibrated routinely for molecular weight determinations with a mixture of standard proteins. Molecular weight estimations of hordeins were performed by evaluation of the relationship between log (MW) versus log (R1) and reproducible linear calibration curves and molecular weight estimates for hordeins (CV 0.66%) were obtained. Densitometric analysis of protein band intensities revealed considerable variability in protein staining. Electrophoretic analysis of 100 barley cultivars revealed that, in general, resolution of SDSGPAGE was superior to that of acidic PAGE but considerable duplication of protein patterns among cultivars and their biotypes remained a problem. Cultivar formulae consisting of B, C and D hordein pattern designations were used to prepare a cultivar catalogue of protein patterns. Sixty-five formulae consisting of 30 B, 36 C and 3 D hordein patterns were obtained. SDSGPAGE also was found suitable for barley malt cultivar analysis.Key words: SDS gradient PAGE, barley, cultivar identification, hordein
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Zhou, Tianfeng, Ying Wang, Jiangtao Che, Benshuai Ruan, Jinxiang Liu, and Xibin Wang. "Surface Microtexture Fabrication and Temperature Gradient Regulation of Micro Wankel Engine." Energies 12, no. 19 (September 29, 2019): 3725. http://dx.doi.org/10.3390/en12193725.
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Nowadays, micro engine miniaturization is one of the most challenging issues, especially for the design and fabrication of the high-power-density micro Wankel engine. With the decrease of the size of the micro engine, the problem of the heat deformation of the cylinder becomes more serious. In this paper, a micro Wankel engine with microtextures on the outer surface of the cylinder is designed and manufactured to diffuse the heat dissipation and regulate the temperature gradient, so as to increase the power output density. First, a series of finite element simulations are conducted to design a type of ideal surface microtexture. Then, the machining condition is optimized to fabricate microtextures by micro cutting on the cylinder surface by studying the processing parameters. Finally, the performance of the new micro Wankel engine in terms of the temperature gradient regulation and the mechanical power output is tested and compared with that of the un-textured micro engine. The comparison results show that temperature of the textured micro engine was dropped from 185 °C to 125 °C and the mechanical power output increased by 10.74% from that of its un-textured counterpart, verifying the proposed methods for temperature gradient regulation.
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Atifi, Khalid, El-Hassan Essoufi, and Bouchra Khouiti. "An inverse backward problem for degenerate two-dimensional parabolic equation." Opuscula Mathematica 40, no. 4 (2020): 427–49. http://dx.doi.org/10.7494/opmath.2020.40.4.427.
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This paper deals with the determination of an initial condition in the degenerate two-dimensional parabolic equation \[\partial_{t}u-\mathrm{div}\left(a(x,y)I_2\nabla u\right)=f,\quad (x,y)\in\Omega,\; t\in(0,T),\] where \(\Omega\) is an open, bounded subset of \(\mathbb{R}^2\), \(a \in C^1(\bar{\Omega})\) with \(a\geqslant 0\) everywhere, and \(f\in L^{2}(\Omega \times (0,T))\), with initial and boundary conditions \[u(x,y,0)=u_0(x,y), \quad u\mid_{\partial\Omega}=0,\] from final observations. This inverse problem is formulated as a minimization problem using the output least squares approach with the Tikhonov regularization. To show the convergence of the descent method, we prove the Lipschitz continuity of the gradient of the Tikhonov functional. Also we present some numerical experiments to show the performance and stability of the proposed approach.
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Moudafi, Abdellatif, and Eman Al-Shemas. "A Penalization-Gradient Algorithm for Variational Inequalities." International Journal of Mathematics and Mathematical Sciences 2011 (2011): 1–12. http://dx.doi.org/10.1155/2011/305856.
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This paper is concerned with the study of a penalization-gradient algorithm for solving variational inequalities, namely, findx̅∈Csuch that〈Ax̅,y-x̅〉≥0for ally∈C, whereA:H→His a single-valued operator,Cis a closed convex set of a real Hilbert spaceH. GivenΨ:H→R ∪ {+∞}which acts as a penalization function with respect to the constraintx̅∈C, and a penalization parameterβk, we consider an algorithm which alternates a proximal step with respect to∂Ψand a gradient step with respect toAand reads asxk=(I+λkβk∂Ψ)-1(xk-1-λkAxk-1). Under mild hypotheses, we obtain weak convergence for an inverse strongly monotone operator and strong convergence for a Lipschitz continuous and strongly monotone operator. Applications to hierarchical minimization and fixed-point problems are also given and the multivalued case is reached by replacing the multivalued operator by its Yosida approximate which is always Lipschitz continuous.
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Cho, Young, and Yook-Kong Yong. "A multi-mesh, preconditioned conjugate gradient solver for eigenvalue problems in finite element models." Computers & Structures 58, no. 3 (February 1996): 575–83. http://dx.doi.org/10.1016/0045-7949(95)00157-c.
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Li, Ye. "An Adaptive Finite Element Method with Hybrid Basis for Singularly Perturbed Nonlinear Eigenvalue Problems." Communications in Computational Physics 19, no. 2 (February 2016): 442–72. http://dx.doi.org/10.4208/cicp.021114.140715a.
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AbstractIn this paper, we propose an uniformly convergent adaptive finite element method with hybrid basis (AFEM-HB) for the discretization of singularly perturbed nonlinear eigenvalue problems under constraints with applications in Bose-Einstein condensation (BEC) and quantum chemistry. We begin with the time-independent Gross-Pitaevskii equation and show how to reformulate it into a singularly perturbed nonlinear eigenvalue problem under a constraint. Matched asymptotic approximations for the problem are reviewed to confirm the asymptotic behaviors of the solutions in the boundary/interior layer regions. By using the normalized gradient flow, we propose an adaptive finite element with hybrid basis to solve the singularly perturbed nonlinear eigenvalue problem. Our basis functions and the mesh are chosen adaptively to the small parameter ε. Extensive numerical results are reported to show the uniform convergence property of our method. We also apply the AFEM-HB to compute the ground and excited states of BEC with box/harmonic/optical lattice potential in the semiclassical regime (0 <ε≪C 1). In addition, we give a detailed error analysis of our AFEM-HB to a simpler singularly perturbed two point boundary value problem, show that our method has a minimum uniform convergence order
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Klyachkin, A. V. "Convection and its Stability in the Equatorial Regions of the Convection Zone." Symposium - International Astronomical Union 138 (1990): 325–28. http://dx.doi.org/10.1017/s0074180900044296.
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The problem of the existence, evolution, and stability of spatial structures in convection is of considerable importance to astrophysics as well as to geophysical hydrodynamics. The Boussinesq approximation will be used because the considered motions in stars are sufficiently slow. The system of hydrodynamic equations describing convection in a rotating inhomogeneous medium has the form: Here Dt is the total time derivative, U the velocity, P, T, and C the deviations of the pressure, temperature, and helium abundance (by mass) from the basic equilibrium values, ρm, νm, χm, and Dm the values averaged over the considered layer of the density, viscosity, thermal and helium diffusivities, βT and βc the averaged coefficients of the thermal and helium expansions, g and Ω the gravitational acceleration and angular velocity, ∇Tb, and ∇Cb the values of the basic equilibrium temperature and helium gradients, and ñTad the adiabatic temperature gradient.
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Arif, Ghassan E., Farah Aini Abdullah, and Y. Al-Douri. "Modeling of the Electronic Properties of Hexagonal Semiconductors." Advanced Materials Research 925 (April 2014): 364–68. http://dx.doi.org/10.4028/www.scientific.net/amr.925.364.
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This paper seeks to investigate the solvability of physical problem by utilizing the mathematical theory of differential equation. A new mathematical model based on mathematical modeling and differential equation is created. The objectives of this work sets up to model ionicity factor based on lattice constants (c/a) of hexagonal structure semiconductors using density functional theory (DFT) of full-potential linear augmented plane wave (FP-LAPW) within Engel Vosko-General Gradient Approximation (EV-GGA). Our determined values are in agreement with experimental and theoretical results.
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Posypkin, Mikhail, and Alexander Usov. "Implementation and verification of global optimization benchmark problems." Open Engineering 7, no. 1 (December 29, 2017): 470–78. http://dx.doi.org/10.1515/eng-2017-0050.
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AbstractThe paper considers the implementation and verification of a test suite containing 150 benchmarks for global deterministic box-constrained optimization. A C++ library for describing standard mathematical expressions was developed for this purpose. The library automate the process of generating the value of a function and its’ gradient at a given point and the interval estimates of a function and its’ gradient on a given box using a single description. Based on this functionality, we have developed a collection of tests for an automatic verification of the proposed benchmarks. The verification has shown that literary sources contain mistakes in the benchmarks description. The library and the test suite are available for download and can be used freely.
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Lyu, Xing-long, Tiexiang Li, Tsung-ming Huang, Jia-wei Lin, Wen-wei Lin, and Sheng Wang. "FAME." ACM Transactions on Mathematical Software 47, no. 3 (June 25, 2021): 1–24. http://dx.doi.org/10.1145/3446329.
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In this article, we propose the Fast Algorithms for Maxwell’s Equations (FAME) package for solving Maxwell’s equations for modeling three-dimensional photonic crystals. FAME combines the null-space free method with fast Fourier transform (FFT)-based matrix-vector multiplications to solve the generalized eigenvalue problems (GEPs) arising from Yee’s discretization. The GEPs are transformed into a null-space free standard eigenvalue problem with a Hermitian positive-definite coefficient matrix. The computation times for FFT-based matrix-vector multiplications with matrices of dimension 7 million are only 0.33 and 3.6 × 10 − 3 seconds using MATLAB with an Intel Xeon CPU and CUDA C++ programming with a single NVIDIA Tesla P100 GPU, respectively. Such multiplications significantly reduce the computational costs of the conjugate gradient method for solving linear systems. We successfully use FAME on a single P100 GPU to solve a set of GEPs with matrices of dimension more than 19 million, in 127 to 191 seconds per problem. These results demonstrate the potential of our proposed package to enable large-scale numerical simulations for novel physical discoveries and engineering applications of photonic crystals.
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Goldner, A., N. Herold, and M. Huber. "The challenge of simulating the warmth of the mid-Miocene climatic optimum in CESM1." Climate of the Past 10, no. 2 (March 13, 2014): 523–36. http://dx.doi.org/10.5194/cp-10-523-2014.
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Abstract. The mid-Miocene climatic optimum (MMCO) is an intriguing climatic period due to its above-modern temperatures in mid-to-high latitudes in the presence of close-to-modern CO2 concentrations. We use the recently released Community Earth System Model (CESM1.0) with a slab ocean to simulate this warm period, incorporating recent Miocene CO2 reconstructions of 400 ppm (parts per million). We simulate a global mean annual temperature (MAT) of 18 °C, ~4 °C above the preindustrial value, but 4 °C colder than the global Miocene MAT we calculate from climate proxies. Sensitivity tests reveal that the inclusion of a reduced Antarctic ice sheet, an equatorial Pacific temperature gradient characteristic of a permanent El Niño, increased CO2 to 560 ppm, and variations in obliquity only marginally improve model–data agreement. All MMCO simulations have an Equator to pole temperature gradient that is at least ~10 °C larger than that reconstructed from proxies. The MMCO simulation most comparable to the proxy records requires a CO2 concentration of 800 ppm. Our results illustrate that MMCO warmth is not reproducible using the CESM1.0 forced with CO2 concentrations reconstructed for the Miocene or including various proposed Earth system feedbacks; the remaining discrepancy in the MAT is comparable to that introduced by a CO2 doubling. The model's tendency to underestimate proxy derived global MAT and overestimate the Equator to pole temperature gradient suggests a major climate problem in the MMCO akin to those in the Eocene. Our results imply that this latest model, as with previous generations of climate models, is either not sensitive enough or additional forcings remain missing that explain half of the anomalous warmth and pronounced polar amplification of the MMCO.
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Dao, Nguyen Anh, Jesus Ildefonso Díaz, and Quan Ba Hong Nguyen. "Pointwise Gradient Estimates in Multi-dimensional Slow Diffusion Equations with a Singular Quenching Term." Advanced Nonlinear Studies 20, no. 2 (May 1, 2020): 477–502. http://dx.doi.org/10.1515/ans-2020-2076.
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AbstractWe consider the high-dimensional equation {\partial_{t}u-\Delta u^{m}+u^{-\beta}{\chi_{\{u>0\}}}=0}, extending the mathematical treatment made in 1992 by B. Kawohl and R. Kersner for the one-dimensional case. Besides the existence of a very weak solution {u\in\mathcal{C}([0,T];L_{\delta}^{1}(\Omega))}, with {u^{-\beta}\chi_{\{u>0\}}\in L^{1}((0,T)\times\Omega)}, {\delta(x)=d(x,\partial\Omega)}, we prove some pointwise gradient estimates for a certain range of the dimension N, {m\geq 1} and {\beta\in(0,m)}, mainly when the absorption dominates over the diffusion ({1\leq m<2+\beta}). In particular, a new kind of universal gradient estimate is proved when {m+\beta\leq 2}. Several qualitative properties (such as the finite time quenching phenomena and the finite speed of propagation) and the study of the Cauchy problem are also considered.
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Oglezneva, Svetlana A., Maxim N. Kachenyuk, Andrey A. Smetkin, and Vadim V. Savich. "Functional Gradient Heat-Resistant Materials Manufactured by Spark Plasma Sintering." Materials Science Forum 1037 (July 6, 2021): 464–72. http://dx.doi.org/10.4028/www.scientific.net/msf.1037.464.
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The objects of the study were powder samples PV-NiCr16Al6Y and PV-Ni75Al23W, intended for the formation of a sublayer in heat-shielding coatings. The aim of this work is to develop and study a sublayer with a complexly organized structure of a functionally graded material of the superalloy-sublayer-ceramic system for operation under thermal cyclic loads and high-temperature gas corrosion. Experimental samples of binding materials for heat-protective coatings (HPC) were obtained by the method of spark plasma sintering (SPS) at T = 1050 °C / 15-30 MPa / 5 min. Methods of laser diffraction, X-ray structural analysis, optical and scanning electron microscopy, X-ray fluorescence spectroscopy, microdurometry were used to study powders and consolidated materials. It is shown that irregular powders contain individual particles of some components - in PV-NiCr16Al6Y powder these are particles of chromium and yttrium, in PV-Ni75Al23W - tungsten and chromium. Consolidated sublayers of such powders exhibit inhomogeneity and irregular porosity. To solve the problem of forming a homogeneous binder sublayer, mechanical alloying of the powders before sintering is proposed. It was found that MA increases the homogeneity of the structure, excludes local inclusions of unreacted particles, and increases the activation of consolidation. MA and subsequent sintering opens up wide possibilities for controlling the structure, including the porosity of the sublayers, and specifying various options for the HPC architecture. Experimental samples of HPC on an Inconel 625 substrate with a mechanically activated PV-Ni75Al23W sublayer and dioxides Zr/Y (YSZ) outer ceramics were obtained by the SPS method. A model of the architecture of a HPC made of a layered binder with different porosities is proposed.
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Ohashi, Asuka, and Tomohiro Sogabe. "Numerical Algorithms for Computing an Arbitrary Singular Value of a Tensor Sum." Axioms 10, no. 3 (August 31, 2021): 211. http://dx.doi.org/10.3390/axioms10030211.
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We consider computing an arbitrary singular value of a tensor sum: T:=In⊗Im⊗A+In⊗B⊗Iℓ+C⊗Im⊗Iℓ∈Rℓmn×ℓmn, where A∈Rℓ×ℓ, B∈Rm×m, C∈Rn×n. We focus on the shift-and-invert Lanczos method, which solves a shift-and-invert eigenvalue problem of (TTT−σ˜2Iℓmn)−1, where σ˜ is set to a scalar value close to the desired singular value. The desired singular value is computed by the maximum eigenvalue of the eigenvalue problem. This shift-and-invert Lanczos method needs to solve large-scale linear systems with the coefficient matrix TTT−σ˜2Iℓmn. The preconditioned conjugate gradient (PCG) method is applied since the direct methods cannot be applied due to the nonzero structure of the coefficient matrix. However, it is difficult in terms of memory requirements to simply implement the shift-and-invert Lanczos and the PCG methods since the size of T grows rapidly by the sizes of A, B, and C. In this paper, we present the following two techniques: (1) efficient implementations of the shift-and-invert Lanczos method for the eigenvalue problem of TTT and the PCG method for TTT−σ˜2Iℓmn using three-dimensional arrays (third-order tensors) and the n-mode products, and (2) preconditioning matrices of the PCG method based on the eigenvalue and the Schur decomposition of T. Finally, we show the effectiveness of the proposed methods through numerical experiments.
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Liu, Bowen, Ting Zhang, Yujian Li, Zhaoying Liu, and Zhilin Zhang. "Kernel Probabilistic K-Means Clustering." Sensors 21, no. 5 (March 8, 2021): 1892. http://dx.doi.org/10.3390/s21051892.
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Kernel fuzzy c-means (KFCM) is a significantly improved version of fuzzy c-means (FCM) for processing linearly inseparable datasets. However, for fuzzification parameter m=1, the problem of KFCM (kernel fuzzy c-means) cannot be solved by Lagrangian optimization. To solve this problem, an equivalent model, called kernel probabilistic k-means (KPKM), is proposed here. The novel model relates KFCM to kernel k-means (KKM) in a unified mathematic framework. Moreover, the proposed KPKM can be addressed by the active gradient projection (AGP) method, which is a nonlinear programming technique with constraints of linear equalities and linear inequalities. To accelerate the AGP method, a fast AGP (FAGP) algorithm was designed. The proposed FAGP uses a maximum-step strategy to estimate the step length, and uses an iterative method to update the projection matrix. Experiments demonstrated the effectiveness of the proposed method through a performance comparison of KPKM with KFCM, KKM, FCM and k-means. Experiments showed that the proposed KPKM is able to find nonlinearly separable structures in synthetic datasets. Ten real UCI datasets were used in this study, and KPKM had better clustering performance on at least six datsets. The proposed fast AGP requires less running time than the original AGP, and it reduced running time by 76–95% on real datasets.
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Negahdari, Zahra, Monika Willert-Porada, and Florian Scherm. "Development of Novel Functionally Graded Al2O3-Lanthanum Hexaaluminate Ceramics for Thermal Barrier Coatings." Materials Science Forum 631-632 (October 2009): 97–102. http://dx.doi.org/10.4028/www.scientific.net/msf.631-632.97.
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Lanthanum hexaaluminate (LHA) has superior thermo-chemical stability at temperatures higher than 1000 °C and is a promising competitor to Y-ZrO2-based thermal barrier coatings (TBCs). The yet unresolved problem is control of microstructure of high LHA content ceramics and adjustment of porosity upon, to arrive at a material exhibiting low thermal conductivity at high temperature combined with structural reliability. Therefore, a functionally graded alumina/lanthanum hexaaluminate (FGLHA) with a gradient in composition was developed. The thermal diffusivity and thermal conductivity of FGLHA were compared with the one of the monolithic composite ceramics. The alumina-rich composites showed excellent mechanical properties whereas the LHA-rich composites presented lower thermal conductivity.
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Liu, Yang, Hong Li, Wei Gao, Siriguleng He, and Zhichao Fang. "A Novel Characteristic Expanded Mixed Method for Reaction-Convection-Diffusion Problems." Journal of Applied Mathematics 2013 (2013): 1–11. http://dx.doi.org/10.1155/2013/683205.
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A novel characteristic expanded mixed finite element method is proposed and analyzed for reaction-convection-diffusion problems. The diffusion term∇·(a(x,t)∇u)is discretized by the novel expanded mixed method, whose gradient belongs to the square integrable space instead of the classicalH(div;Ω)space and the hyperbolic partd(x)(∂u/∂t)+c(x,t)·∇uis handled by the characteristic method. For a priori error estimates, some important lemmas based on the novel expanded mixed projection are introduced. The fully discrete error estimates based on backward Euler scheme are obtained. Moreover, the optimal a priori error estimates inL2- andH1-norms for the scalar unknownuand a priori error estimates in(L2)2-norm for its gradientλand its fluxσ(the coefficients times the negative gradient) are derived. Finally, a numerical example is provided to verify our theoretical results.
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Golla, Madhu. "A Novel Algorithm for Segmentation of Parasites in Thin Blood Smears From Microscopy Using Type II Fuzzy Sets and Inverse Gaussian Gradient." International Journal of Computer Vision and Image Processing 9, no. 3 (July 2019): 1–22. http://dx.doi.org/10.4018/ijcvip.2019070101.
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Malaria is the leading health problem globally in the equatorial regions. Even after campaigning and control by the World Health Organization (WHO), malaria is a high mortality-causing infectious disease due to inappropriate and late diagnosis. To prevent getting affected by malaria, the diagnosis should be in the early stage and accurate. This research presents an innovative approach for erythrocyte segmentation and malaria parasite detection from microscopic images. In addition, the author utilizes Einstein t-conorm function to generate new fuzzy membership function which is used to segment the infected regions of the blood cells in microscopic images. Finally, the inverse Gaussian gradient function is used for the final segmentation. This technique is compared with state-of-the-art segmentation techniques such as k-means, fuzzy c-means segmentation, and spatial intuitionistic fuzzy c-means (SIFCM) segmentation approaches. Experimental results are validated qualitatively, and it is deduced that the proposed method is the robust segmentation method for malaria parasite detection.
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SAVITHA, R., S. SURESH, and N. SUNDARARAJAN. "A FULLY COMPLEX-VALUED RADIAL BASIS FUNCTION NETWORK AND ITS LEARNING ALGORITHM." International Journal of Neural Systems 19, no. 04 (August 2009): 253–67. http://dx.doi.org/10.1142/s0129065709002026.
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In this paper, a fully complex-valued radial basis function (FC-RBF) network with a fully complex-valued activation function has been proposed, and its complex-valued gradient descent learning algorithm has been developed. The fully complex activation function, sech(.) of the proposed network, satisfies all the properties needed for a complex-valued activation function and has Gaussian-like characteristics. It maps Cn → C, unlike the existing activation functions of complex-valued RBF network that maps Cn → R. Since the performance of the complex-RBF network depends on the number of neurons and initialization of network parameters, we propose a K-means clustering based neuron selection and center initialization scheme. First, we present a study on convergence using complex XOR problem. Next, we present a synthetic function approximation problem and the two-spiral classification problem. Finally, we present the results for two practical applications, viz., a non-minimum phase equalization and an adaptive beam-forming problem. The performance of the network was compared with other well-known complex-valued RBF networks available in literature, viz., split-complex CRBF, CMRAN and the CELM. The results indicate that the proposed fully complex-valued network has better convergence, approximation and classification ability.
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Goldner, A., N. Herold, and M. Huber. "The challenge of simulating warmth of the mid-Miocene Climate Optimum in CESM1." Climate of the Past Discussions 9, no. 3 (June 26, 2013): 3489–518. http://dx.doi.org/10.5194/cpd-9-3489-2013.
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Abstract. The mid-Miocene Climatic Optimum (MMCO) is an intriguing climatic period due to its above-modern temperatures in mid-to-high latitudes in the presence of close-to-modern CO2 concentrations. We use the recently released Community Earth System Model (CESM1.0) with a slab ocean to simulate this warm period, incorporating recent Miocene CO2 reconstructions of 400 ppm. We simulate a global mean annual temperature (MAT) of 18 °C, ~4 °C above the pre-industrial value, but 4 °C colder than the global Miocene MAT we calculate from climate proxies. Sensitivity tests reveal that the inclusion of a reduced Antarctic ice sheet, eastern equatorial Pacific Ocean temperature anomalies, increased CO2 to 560 ppm, and variations in obliquity only marginally improve model-data agreement. All MMCO simulations have an equator to pole temperature gradient which is at least ~ 10 °C larger than the reconstruction from proxies. The MMCO simulation most comparable to the proxy records requires a CO2 concentration of 800 ppm. Our results illustrate that MMCO warmth is not reproducible using the CESM1.0 forced with CO2 concentrations reconstructed for the Miocene or including various proposed Earth system feedbacks; the remaining discrepancy in the MAT is comparable to that introduced by a CO2 doubling. The models tendency to underestimate proxy derived global MAT and overestimate the equator to pole temperature gradient suggests a major climate problem in the MMCO akin to those in the Eocene. Our results imply that this latest model, as with previous generations of climate models, is either not sensitive enough or additional forcings remain missing that explain half of the anomalous warmth and pronounced polar amplification of the MMCO.
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Hosseinzadegan, Samar, Andreas Fhager, Mikael Persson, and Paul Meaney. "A Discrete Dipole Approximation Solver Based on the COCG-FFT Algorithm and Its Application to Microwave Breast Imaging." International Journal of Antennas and Propagation 2019 (July 17, 2019): 1–12. http://dx.doi.org/10.1155/2019/9014969.
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We introduce the discrete dipole approximation (DDA) for efficiently calculating the two-dimensional electric field distribution for our microwave tomographic breast imaging system. For iterative inverse problems such as microwave tomography, the forward field computation is the time limiting step. In this paper, the two-dimensional algorithm is derived and formulated such that the iterative conjugate orthogonal conjugate gradient (COCG) method can be used for efficiently solving the forward problem. We have also optimized the matrix-vector multiplication step by formulating the problem such that the nondiagonal portion of the matrix used to compute the dipole moments is block-Toeplitz. The computation costs for multiplying the block matrices times a vector can be dramatically accelerated by expanding each Toeplitz matrix to a circulant matrix for which the convolution theorem is applied for fast computation utilizing the fast Fourier transform (FFT). The results demonstrate that this formulation is accurate and efficient. In this work, the computation times for the direct solvers, the iterative solver (COCG), and the iterative solver using the fast Fourier transform (COCG-FFT) are compared with the best performance achieved using the iterative solver (COCG-FFT) in C++. Utilizing this formulation provides a computationally efficient building block for developing a low cost and fast breast imaging system to serve under-resourced populations.
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Tong, P., D. Zhao, D. Yang, X. Yang, J. Chen, and Q. Liu. "Wave-equation-based travel-time seismic tomography – Part 1: Method." Solid Earth 5, no. 2 (November 26, 2014): 1151–68. http://dx.doi.org/10.5194/se-5-1151-2014.
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Abstract. In this paper, we propose a wave-equation-based travel-time seismic tomography method with a detailed description of its step-by-step process. First, a linear relationship between the travel-time residual Δt = Tobs–Tsyn and the relative velocity perturbation δ c(x)/c(x) connected by a finite-frequency travel-time sensitivity kernel K(x) is theoretically derived using the adjoint method. To accurately calculate the travel-time residual Δt, two automatic arrival-time picking techniques including the envelop energy ratio method and the combined ray and cross-correlation method are then developed to compute the arrival times Tsyn for synthetic seismograms. The arrival times Tobs of observed seismograms are usually determined by manual hand picking in real applications. Travel-time sensitivity kernel K(x) is constructed by convolving a~forward wavefield u(t,x) with an adjoint wavefield q(t,x). The calculations of synthetic seismograms and sensitivity kernels rely on forward modeling. To make it computationally feasible for tomographic problems involving a large number of seismic records, the forward problem is solved in the two-dimensional (2-D) vertical plane passing through the source and the receiver by a high-order central difference method. The final model is parameterized on 3-D regular grid (inversion) nodes with variable spacings, while model values on each 2-D forward modeling node are linearly interpolated by the values at its eight surrounding 3-D inversion grid nodes. Finally, the tomographic inverse problem is formulated as a regularized optimization problem, which can be iteratively solved by either the LSQR solver or a~nonlinear conjugate-gradient method. To provide some insights into future 3-D tomographic inversions, Fréchet kernels for different seismic phases are also demonstrated in this study.
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Hussain, Bilal, Asif Khan, Nadeem Javaid, Qadeer Hasan, Shahzad A. Malik, Omar Ahmad, Amir Dar, and Ahmad Kazmi. "A Weighted-Sum PSO Algorithm for HEMS: A New Approach for the Design and Diversified Performance Analysis." Electronics 8, no. 2 (February 4, 2019): 180. http://dx.doi.org/10.3390/electronics8020180.
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This research focuses on a decomposed-weighted-sum particle swarm optimization (DWS-PSO) approach that is proposed for optimal operations of price-driven demand response (PDDR) and PDDR-synergized with the renewable and energy storage dispatch (PDDR-RED) based home energy management systems (HEMSs). The algorithm for PDDR-RED-based HEMS is developed by combining a DWS-PSO-based PDDR scheme for load shifting with the dispatch strategy for the photovoltaic (PV), storage battery (SB), and power grid systems. Shiftable home appliances (SHAs) are modeled for mixed scheduling (MS). The MS includes advanced as well as delayed scheduling (AS/DS) of SHAs to maximize the reduction in the net cost of energy ( C E ). A set of weighting vectors is deployed while implementing algorithms and a multi-objective-optimization (MOO) problem is decomposed into single-objective sub-problems that are optimized simultaneously in a single run. Furthermore, an innovative method to carry out the diversified performance analysis (DPA) of the proposed algorithms is also proposed. The method comprises the construction of a diversified set of test problems (TPs), defining of performance metrics, and computation of the metrics. The TPs are constructed for a set of standardized dynamic pricing signal and for scheduling models for MS and DS. The simulation results show the gradient of the tradeoff line for the reduction in C E and related discomfort for DPA.
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Babameto-Laku, A., A. Mitre, S. Berisha, V. Mokini, and D. Roko. "Molecular Genetic Characterization of β-Thalassemia and Sickle Cell Syndrome in the Albanian Population." Balkan Journal of Medical Genetics 14, no. 1 (January 1, 2011): 45–50. http://dx.doi.org/10.2478/v10034-011-0017-0.
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Molecular Genetic Characterization of β-Thalassemia and Sickle Cell Syndrome in the Albanian Populationβ-Thalassemia (β-thal) is a major public health problem in Albania as it is in many Mediterranean countries. We determined the different β-thal alleles that are present in the Albanian population by using the temporal temperature gradient electrophoresis (TTGE) method because of its high throughput, cost-effectiveness, sensitivity and simplicity. DNA from blood of 68 patients with β-thal, 26 with sickle cell anemia or sickle cell β-thal, 54 parents of these patients and 14 heterozygotes related to these families. We found the IVS-I-110 (G>A), codon 39 (C>T), IVS-I-6 (T>C), IVS-I-1 (G>A) and codon 44 (-C) mutations that accounted for nearly 90% of the β-thal alleles. Their frequencies were similar to those found in other studies in the Albanian population. This method has permitted the detection of heterozygotes for β-thal in this population and offers a prenatal diagnosis with a probability of 90% accuracy.
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Toloraya, V. N., and G. A. Ostroukhova. "Production of single-crystal seeds [001] from nickeltungsten alloys by directional crystallization." Voprosy Materialovedeniya, no. 2(106) (August 1, 2021): 55–65. http://dx.doi.org/10.22349/1994-6716-2021-106-2-55-65.
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The problem of obtaining priming materials from Ni-W alloys arose in connection with the development of technology for casting single-crystal turbine blades of gas turbine engines (GTE) from hightemperature alloys. This technology uses a seed method for producing single-crystal castings with a crystallographic orientation [001] using seedings from alloys of the Ni-W system with a melting point 120–140°C higher than the casting alloy. The use of such primers greatly simplifies the casting process of turbine blades with a single-crystal structure, increases its reliability both in pass-through furnaces of the PMP-2 type and in high-gradient furnaces of the UVNK-9A type. The article presents the results of the study of the influence of temperature-velocity parameters of directional crystallization, namely, the temperature gradient GZ on the structure of the obtained single-crystal seed blanks, as well as the study of effects of tungsten and carbon on the structure of single-crystal seed blanks, and makes recommendations for optimizing the technological process of single-crystal casting of Ni–W seed blanks adjusting the alloy composition for the seed blanks.
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WOO, DONG-MIN, DONG-CHUL PARK, and QUOC-DAT NGUYEN. "TERRAIN CLASSIFICATION USING 3D CO-OCCURRENCE FEATURES AND NEURAL NETWORKS." International Journal of Information Acquisition 04, no. 04 (December 2007): 317–25. http://dx.doi.org/10.1142/s0219878907001381.
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Texture analysis has been efficiently utilized in the area of terrain classification. In this application, features have been obtained in the 2D image domain. In this paper we suggest 3D co-occurrence texture features by extending the concept of co-occurrence feature to the 3D world. The suggested 3D features are described as a 3D co-occurrence matrix by using a co-occurrence histogram of digital elevations at two contiguous positions. The practical construction of the co-occurrence matrix limits the number of levels of digital elevation. If the digital elevation is quantized into a few levels over the whole DEM (Digital Elevation Map), distinctive features cannot be obtained. To resolve this quantization problem, we employ the local quantization technique which can preserve the variation of elevations with a small number of quantization levels. SOM (Self-Organizing Maps), FCM (Fuzzy C-mean) and GBFCM (Gradient Based Fuzzy C-mean) clustering algorithms are employed to implement the terrain classifier, since these ANN clustering algorithms are known as robust against the high dimensionality problem in the classification process. Experimental results show that the classification accuracy with the addition of 3D co-occurrence features is significantly improved over the conventional classification method only with 2D features.
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Russo, S. P., A. S. Barnard, and I. K. Snook. "Hydrogenation of Nanodiamond Surfaces: Structure and Effects on Crystalline Stability." Surface Review and Letters 10, no. 02n03 (April 2003): 233–39. http://dx.doi.org/10.1142/s0218625x03004998.
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Presented are results of our ab initio study of the surface reconstruction and relaxation of (100) surfaces on bulk and nanocrystalline diamond. We have used a density functional theory (DFT) within the generalized-gradient approximation (GGA) via the parallel computer version of the Vienna ab initio simulation package (VASP), to consider dehydrogenated and hydrogenated surfaces. Edges and corners of nanocrystals offer a new challenge in the determination of surface structure. We have applied the methodology for stepped diamond (100) surfaces to this problem, and consider it useful in describing nanodiamond edges and corners to first approximation. Our results also indicate that dimer lengths and atomic layer depths of the C(100)(2 × 1) and C(100)(2 × 1):H nanodiamond surfaces differ slightly from those of bulk diamond. The effects of these differences on crystalline stability are discussed, with the intension of offering a better understanding of the effects of nanodiamond surfaces on the stability of diamondoid nanostructures.
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Akram, Safia, Najma Saleem, Mir Yasir Umair, and Sufian Munawar. "Impact of partial slip and lateral walls on peristaltic transport of a couple stress fluid in a rectangular duct." Science Progress 104, no. 2 (April 2021): 003685042110136. http://dx.doi.org/10.1177/00368504211013632.
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The impact of lateral walls and partial slip with different waveforms on peristaltic pumping of couple stress fluid in a rectangular duct with different waveforms has been discussed in the current article. By means of a wave frame of reference the flow is explored travelling away from a fixed frame with velocity c. Peristaltic waves generated on horizontal surface walls of rectangular duct are considered using lubrication technique. Mathematical modelling of couple fluid for three-dimensional flow are first discussed in detail. Lubrication approaches are used to simplify the proposed problem. Exact solutions of pressure gradient, pressure rise, velocity and stream function have been calculated. Numerical and graphical descriptions are displayed to look at the behaviour of diverse emerging parameters.
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Kőszegi, B., and G. Kovács. "Gradient chamber studies on the dry matter accumulation of winter emmer [Triticum turgidum ssp. dicoccon (Schrank) Thell.] landraces in the seedling stage." Acta Agronomica Hungarica 51, no. 4 (December 1, 2003): 413–18. http://dx.doi.org/10.1556/aagr.51.2003.4.6.
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The multiplication and characterisation of genetic stocks originating under very different ecological conditions is a problem constantly encountered in gene bank research. However, the major components of the original environment, such as temperature, light and humidity, can be reproduced under artificial conditions in the phytotron. The gradient, or inhomogeneous, chamber available in the phytotron of the Agricultural Research Institute of the Hungarian Academy of Sciences, Martonvásár, makes it possible to elaborate plant growth programmes optimised for the various developmental phases of each population in a single step. In this chamber gradients of two extremely important environmental factors, temperature and illumination, can be simultaneously programmed, thus allowing the optimum light × heat combinations to be identified. However, the use of complete inhomogeneity (light × heat) makes it extremely difficult to evaluate the experimental results, since biometric methods based on traditional statistics are unable to handle this situation. It is thus essential to find a method suitable for the comparative analysis of continual variables (Okada et al., 2000). The present paper reports on the first phase in the development of a plant growth programme for emmer, based on investigations made on two gene bank accessions of winter Triticum turgidum ssp. dicoccon (Schrank) Thell. (MvGB 301 and MvGB 304). In the gradient chamber study the accumulation of dry biomass in three-week-old plants was investigated as a function of temperature and light intensity. The results suggest that a temperature of 10-12°C combined with low or moderate light intensity is optimum for the germination and initial development (0-4 weeks) of emmer. These conditions also induced good tillering, which is extremely important, especially for gene bank accessions where the possibility of seed multiplication and field cultivation is limited.
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Bildhauer, M., M. Fuchs, and Giuseppe Mingione. "A Priori Gradient Bounds and Local $C^{1, \alpha}$-Estimates for (Double) Obstacle Problems under Non-Standard Growth Conditions." Zeitschrift für Analysis und ihre Anwendungen 20, no. 4 (2001): 959–85. http://dx.doi.org/10.4171/zaa/1054.
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DeGroot, Christopher. "Convergence and error analysis of an automatically differentiated finite volume based heat conduction code." International Journal of Numerical Methods for Heat & Fluid Flow 29, no. 7 (July 1, 2019): 2389–406. http://dx.doi.org/10.1108/hff-09-2018-0489.
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Purpose This paper aims to investigate the convergence and error properties of a finite volume-based heat conduction code that uses automatic differentiation to evaluate derivatives of solutions outputs with respect to arbitrary solution input(s). A problem involving conduction in a plane wall with convection at its surfaces is used as a test problem, as it has an analytical solution, and the error can be evaluated directly. Design/methodology/approach The finite volume method is used to discretize the transient heat diffusion equation with constant thermophysical properties. The discretized problem is then linearized, which results in two linear systems; one for the primary solution field and one for the secondary field, representing the derivative of the primary field with respect to the selected input(s). Derivatives required in the formation of the secondary linear system are obtained by automatic differentiation using an operator overloading and templating approach in C++. Findings The temporal and spatial discretization error for the derivative solution follows the same order of accuracy as the primary solution. Second-order accuracy of the spatial and temporal discretization schemes is confirmed for both primary and secondary problems using both orthogonal and non-orthogonal grids. However, it has been found that for non-orthogonal cases, there is a limit to the error reduction, which is concluded to be a result of errors in the Gauss-based gradient reconstruction method. Originality/value The convergence and error properties of derivative solutions obtained by forward mode automatic differentiation of finite volume-based codes have not been previously investigated.