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A novel physics-regularized interpretable machine learning model for grain growth
Not Available
An iterative reconstruction algorithm for pole figure inversion using total variation regularization
This paper describes a new discrete method for inverting X-ray pole figures to estimate the orientation distribution function (ODF). The method employs the equal-volume `cubochoric' representation for uniform discretization of orientation space, SO(3). The forward-projection model is combined with an anisotropic total variation term to iteratively determine the ODF. Here, the efficacy of the new method is evaluated with both model and experimental data and compared with existing discrete and series expansion methods.
Domain Decomposition for Integer Optimal Control with Total Variation Regularization
Total variation integer optimal control problems admit solutions and necessary optimality conditions via geometric variational analysis. In spite of the existence of said solutions, algorithms which solve the discretized objective suffer from high numerical cost associated with the combinatorial nature of integer programming. Hence, such methods are often limited to small and medium-sized problems. We propose a globally convergent, coordinate descent–inspired algorithm that allows tractable subproblem solutions restricted to a partition of the domain. Our decomposition method solves relatively small trust-region subproblems that modify the control variable on a subdomain only. Given nontrivial subdomain overlap, we prove that a global first-order necessary optimality condition is equivalent to a first-order necessary optimality condition per subdomain. We additionally show that a sufficient decrease is achieved on a single subdomain by way of a trust-region subproblem solver using geometric measure–theoretic arguments, which we integrate with a greedy patch selection to prove convergence of our algorithm. In conclusion, we demonstrate the practicality of our algorithm on a benchmark large-scale, PDE-constrained integer optimal control problem and find that our method is faster than the state of the art.
On arbitrarily regular conforming virtual element methods for elliptic partial differential equations
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A Probabilistic Approach to Interior Regularity of Fully Nonlinear Degenerate Elliptic Equations in Smooth Domains
We consider the value function of a stochastic optimal control of degenerate diffusion processes in a domain D. We study the smoothness of the value function, under the assumption of the non-degeneracy of the diffusion term along the normal to the boundary and an interior condition weaker than the non-degeneracy of the diffusion term. When the diffusion term, drift term, discount factor, running payoff and terminal payoff are all in the class of C{sup 1,1}( D-bar ) , the value function turns out to be the unique solution in the class of C{sub loc}{sup 1,1}(D) Intersection C{sup 0,1}( D-bar ) to the associated degenerate Bellman equation with Dirichlet boundary data. Our approach is probabilistic.
Global Existence and Uniqueness of Weak and Regular Solutions of Shallow Shells with Thermal Effects
We study a dynamical thin shallow shell whose elastic deformations are described by a nonlinear system of Marguerre–Vlasov’s type under the presence of thermal effects. Our main result is the proof of a global existence and uniqueness of a weak solution in the case of clamped boundary conditions. Standard techniques for uniqueness do not work directly in this case. We overcame this difficulty using recent work due to Lasiecka (Appl Anal 4:1376–1422, 1998).
Block Matching Local SVD Operator Based Sparsity and TV Regularization for Image Denoising
Not provided.
Regularity of the Speed of Biased Random Walk in a One-Dimensional Percolation Model
We consider biased random walks on the infinite cluster of a conditional bond percolation model on the infinite ladder graph. Axelson-Fisk and Häggström established for this model a phase transition for the asymptotic linear speed v̄ of the walk. Namely, there exists some critical value λ{sub c}>0 such that v̄>0 if λ∈(0,λ{sub c}) and v̄=0 if λ≥λ{sub c}. We show that the speed v̄ is continuous in λ on (0,∞) and differentiable on (0,λ{sub c}/2). Moreover, we characterize the derivative as a covariance. For the proof of the differentiability of v̄ on (0,λ{sub c}/2), we require and prove a central limit theorem for the biased random walk. Additionally, we prove that the central limit theorem fails to hold for λ≥λ{sub c}/2.
A{sub 1}-Regularity and Boundedness of Riesz Transforms in Banach Lattices of Measurable Functions
Let X be a Banach lattice of measurable functions on ℝ{sup n} × Ω having the Fatou property. We show that the boundedness of all Riesz transforms R{sub j} in X is equivalent to the boundedness of the Hardy–Littlewood maximal operator M in both X and X′, and thus to the boundedness of all Calderón–Zygmund operators in X. We also prove a result for the case of operators between lattices: If Y ⊃ X is a Banach lattice with the Fatou property such that the maximal operator is bounded in Y ′, then the boundedness of all Riesz transforms from X to Y is equivalent to the boundedness of the maximal operator from X to Y , and thus to the boundedness of all Calderón–Zygmund operators from X to Y .
Regularity of Maximum Distance Minimizers
We study properties of sets having the minimum length (one-dimensional Hausdorff measure) in the class of closed connected sets Σ ⊂ ℝ{sup 2} satisfying the inequality max{sub yϵM} dist (y, Σ) ≤ r for a given compact set M ⊂ ℝ{sup 2} and given r > 0. Such sets play the role of the shortest possible pipelines arriving at a distance at most r to every point of M where M is the set of customers of the pipeline.In this paper, it is announced that every maximum distance minimizer is a union of finitely many curves having one-sided tangent lines at every point. This shows that a maximum distance minimizer is isotopic to a finite Steiner tree even for a “bad” compact set M, which distinguishes it from a solution of the Steiner problem (an example of a Steiner tree with infinitely many branching points can be found in a paper by Paolini, Stepanov, and Teplitskaya). Moreover, the angle between these lines at each point of a maximum distance minimizer is at least 2π/3. Also, we classify the behavior of a minimizer Σ in a neighborhood of any point of Σ. In fact, all the results are proved for a more general class of local minimizers.
On Regularity of Solutions for Initial-Boundary Value Problems for the Zakharov–Kuznetsov Equation
No abstract prepared.
Nonlinear Regularization of Inverse Problems for Linear Homogeneous Transforms by Stabilized Hard Thresholding
In this paper we consider the problem of inverting linear homogeneous transforms by Vaguelette–Wavelet decomposition and stabilized hard thresholding of noisy wavelet coefficients. We also prove asymptotic normality and strong consistency of the mean-square risk estimate for this method.
Regularities and Mechanisms of Formation of Submicro-, Nano-, and Ultrafine-Grained Structures and Mechanical Properties of Metals and Alloys Under Different Treatments
An overview of our original studies and the results reported in the literature on the investigation of variations in structure, phase composition, mechanical and other properties of metallic materials under external impacts is made, including their high-pressure processing by large (severe) plastic and megaplastic deformation, explosion loading, and irradiation with ultra-short laser pulses.
Regularities of Plasma-Immersion Formation of Long-Pulse High-Intensity Titanium Ion Beams
The results of experimental investigations on plasma-immersion formation of ballistically focused beams of low-energy titanium ions with the pulse duration up to 30 μs are presented. The processes of neutralization of the space charge of high-intensity beams upon increasing the ion-current density by a few orders of magnitude during their focusing are addressed. The conditions of preliminary injection of the metal plasma, its parameters, the formation of the beam plasma during residual-gas ionization and secondary and thermionic emissions are shown to be of critical importance for an effective transport of these beams in the equi-potential drift space. It is demonstrated that the use of a disc electrode, preventing the macroparticles from penetrating the region of the ballistic beam focusing, increases the efficiency of long-pulse titanium ion beam transport and simultaneously reduces the probability of instability development.
Phase and defect diagrams based on spectral grain boundary segregation: A regular solution approach
Not provided.