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At least 217 records · Page 12

Regularity of Solutions to Quasilinear Parabolic Systems with Time-Nonsmooth Principal Matrix and the Neumann Boundary Condition

We consider a quasilinear parabolic system of equations with nondiagonal principal matrix in a model parabolic cylinder with the Neumann condition on the plane part Γ of the lateral surface of the cylinder. We prove the partial regularity (the Hölder continuity) of the weak solution in a neighborhood of Γ by the method of A(t)-caloric approximations adapted to the problem with the Neumann boundary condition.

97 MATHEMATICS AND COMPUTING↗

Effective Thermal Contact Resistance of Regularly Textured Bodies in the Presence of Intercontact Heat-Conducting Media and the Phenomenon of Thermal Rectification

We compute the effective thermal contact resistance of a pair of materials formed by AISI 304 stainless steel and 200 nickel alloy in the presence of a periodic array of gaps filled with a heat-conducting medium (argon, water, helium, oxygen, or air) on the interface of these materials. In the nondeformed state, the surface of AISI 304 stainless steel has a microtextured topography formed by regularly located grooves of identical shapes, while the surface of 200 nickel alloy is perfectly flat. We estimate the level of thermal rectification for structures of this kind for different values of the applied mechanical and thermal loads and the maximal height of the surface grooves.

42 ENGINEERING↗

On Dimensional Regularization in the Yang–Mills Theory

We suggest an asymptotic approach to renormalization in the case of dimensional regularization. As an example, the quantum Yang–Mills theory in the four-dimensional space-time is considered. A formula for the renormalized effective action is derived by using the asymptotic behavior of the bare coupling constant. Then we discuss the dimensional transmutation, the process of renormalization, and the properties of the coupling constant.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Physicochemical regularities of strontium sorption by sorbents based on di(tert-butyldicyclohexano)-18-crown-6

A number of sorbents based on di(tert-butyldicyclohexano)-18-crown-6, 1,1,7-trihydrododecafluoroheptanol, and various supports (Porolas-T, LPS-500, hydrophobized silica gel) were prepared. The effect of the supports on strontium sorption from nitric acid solutions was estimated. The physicochemical regularities of strontium sorption (isotherm, kinetics, and selectivity) were studied.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Regularities of salting-out and metal ion extraction by synergistic mixtures of potassium bis(alkylpolyoxyethylene)phosphate and alkylbenzyldimethylammonium chloride under polythermic conditions

The regularities of salting-out of a ionic associate formed by anionic oxyethylated surfactant (potassium bis(alkylpolyoxyethylene)phosphate) and cationic surfactant (alkylbenzyldimethylammonium chloride) with inorganic salts were studied. The possibility of using the ionic associate for thallium(III) and indium extraction in the presence of sodium chloride as a saltingout agent at 60 °C was proved.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Incremental nonnegative matrix factorization based on correlation and graph regularization for matrix completion

Matrix factorization is widely used in recommendation systems, text mining, face recognition and computer vision. As one of the most popular methods, nonnegative matrix factorization and its incremental variants have attracted much attention. The existing incremental algorithms are established based on the assumption of samples are independent and only update the new latent variable of weighting coefficient matrix when the new sample comes, which may lead to inferior solutions. To address this issue, we investigate a novel incremental nonnegative matrix factorization algorithm based on correlation and graph regularizer (ICGNMF). The correlation is mainly used for finding out those correlated rows to be updated, that is, we assume that samples are dependent on each other. We derive the updating rules for ICGNMF by considering the correlation. We also present tests on widely used image datasets, and show ICGNMF reduces the error by comparing other methods.

Zhang, Xiaoxia↗

L{sup ∞} error bound of conservative compact difference scheme for the generalized symmetric regularized long-wave (GSRLW) equations

In this paper, we design a compact finite difference scheme which preserves the original conservative properties to solve the generalized symmetric regularized long-wave equations. The existence of the difference solution is proved by the Brouwer fixed-point theorem. Applying the discrete energy method, the convergence and stability of the difference scheme is obtained, and its numerical convergence order is O(τ{sup 2}+h{sup 4}) in the L{sup ∞}-norm for u and ρ. For computing the nonlinear algebraic system generated by the compact scheme, a decoupled iterative algorithm is constructed and proved to be convergent. Numerical experiment results show that the theory is accurate and the method is efficient and reliable.

97 MATHEMATICS AND COMPUTING↗

On the regularization method for Fredholm integral equations with odd weakly singular kernel

In this paper, we propose a numerical method to approach the solution of a Fredholm integral equation with a weakly singular kernel by applying the convolution product as a regularization operator and the Fourier series as a projection. Preliminary numerical results show that the order of convergence of the method is better than the one of conventional projection methods.

97 MATHEMATICS AND COMPUTING↗

From irregular to regular eutectic growth in the Al-Al 3 Ni system: In situ observations during directional solidification

Here we investigate the irregular eutectic growth dynamics of the Al-Al 3 Ni alloy, in which one of the solid phases (Al 3 Ni) grows faceted from the liquid. Leveraging in situ optical microscopy and synchrotron transmission x-ray microscopy, we address the question of the degree of coupling between Al and Al 3 Ni at the growth front and that of the shape of the microstructures left behind in the bulk solid during directional solidification. Real-time optical observations bring evidence for a morphological transition from a eutectic-grain dependent, irregular eutectic growth at low solidification velocity V (typically 1 μm s -1 ), to a weakly anisotropic, regular growth at higher V ( reaching 10 μm s -1 ). Unprecedented x-ray nano-imaging of the solid–liquid interface, and 3D characterization of the growth patterns, were made possible by a new DS setup at Brookhaven National Laboratory’s NSLS-II. At low V, the leading tips of partly faceted Al 3 Ni crystals are observed to grow not far ahead of the Al growth front. Correlating in situ images and postmortem 3D tomographic reconstructions reveals that the presence of faceted and non-faceted regions of Al 3 Ni crystals in the solid is a direct consequence of coupling and decoupling during DS, respectively. Upon increasing V, the lead distance of Al 3 Ni vanishes, and the shape of Al 3 Ni ceases to be governed by faceted growth. These observations cast light onto the basic mechanisms (faceted growth, diffusive coupling, and the dynamics of trijunctions) governing a faceted to rod-like transition upon increasing V in the Al 3 Ni system, with broad implications to a large class of irregular eutectics.

36 MATERIALS SCIENCE↗

SU(3) quantum spin ladders as a regularization of the CP(2) model at non-zero density: From classical to quantum simulation

Quantum simulations would be highly desirable in order to investigate the finite density physics of QCD. (1+1)-d CP(N−1) quantum field theories are toy models that share many important features of QCD: they are asymptotically free, have a non-perturbatively generated massgap, as well as θ-vacua. SU(N) quantum spin ladders provide an unconventional regularization of CP(N−1) models that is well-suited for quantum simulation with ultracold alkaline-earth atoms in an optical lattice. In order to validate future quantum simulation experiments of CP(2) models at finite density, here we use quantum Monte Carlo simulations on classical computers to investigate SU(3) quantum spin ladders at non-zero chemical potential. This reveals a rich phase structure, with single- or double-species Bose–Einstein “condensates”, with or without ferromagnetic order.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Quasinormal modes for non-minimally coupled scalar fields in regular black hole spacetimes: Grey-body factors, area spectrum and shadow radius

Black hole perturbation theory is a useful approach to study interactions between black holes and fundamental fields. A particular class of black hole solutions arising out of modification of Einstein’s general theory of relativity are regular black holes (RBHs) which can be constructed using a nonlinear electrodynamic Lagrangian. Because of their importance, we are interested in studying the behavior of three kinds of such RBHs under perturbations generated by an external field. Indeed, we investigate the quasinormal modes (QNMs) of a massive scalar field propagating near the RBHs which is non-minimally coupled to the Ricci scalar-tensor of background geometry. We will attempt to find the low-lying quasinormal frequencies of the perturbations by using WKB approximation. We shall also study the relationship between the QNMs and some characteristic properties of black holes such as grey-body factors, area quantization, and shadow radius.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Unconditionally stable, second-order schemes for gradient-regularized, non-convex, finite-strain elasticity modeling martensitic phase transformations

In the setting of continuum elasticity martensitic phase transformations are characterized by a non-convex free energy density function that possesses multiple wells in strain space and includes higher-order gradient terms for regularization. Metastable martensitic microstructures, defined as solutions that are local minimizers of the total free energy, are of interest and are obtained as steady state solutions to the resulting transient formulation of Toupin’s gradient elasticity at finite strain. This type of problem poses several numerical challenges including stiffness, the need for fine discretization to resolve microstructures, and following solution branches. Accurate time-integration schemes are essential to obtain meaningful solutions at reasonable computational cost. Here in this work we introduce two classes of unconditionally stable second-order time-integration schemes for gradient elasticity, each having relative advantages over the other. Numerical examples are shown highlighting these features.

42 ENGINEERING↗

A regularized deconvolution method for turbulent closure modeling in implicitly filtered large-eddy simulation

Turbulence closure models that are based on a regularized deconvolution method (RDM) are proposed for application to implicitly filtered Large-Eddy Simulation (LES). This method reconstructs sub-grid scale contributions by approximately recovering filtered quantities through an optimization approach. Physical principles on the boundedness and conservation of reconstructed quantities are preserved by constraining the optimization problem. Further, to account for effects of scales that are not resolved in implicitly filtered LES, a reconstruction method is proposed that combines sub-grid projection and energy-similarity to enrich unresolved scales. With this method, closure models are developed for turbulent scalar fluxes and turbulence–chemistry interaction that are intrinsically consistent with the LES formulation. These closure models are evaluated in application to a piloted turbulent jet flame with inhomogeneous inlet composition, in which combustion is represented by a two-scalar manifold model. The RDM-formulation is benchmarked against simulations obtained using a presumed PDF method and eddy diffusivity closure model. In partially-premixed flame regions, it is observed that RDM improves the prediction of turbulent mixing, and faster grid convergence is observed for results with RDM compared to simulations employing a presumed PDF method.

42 ENGINEERING↗