L1-type smoothness indicators based weighted essentially nonoscillatory scheme for Hamilton-Jacobi equations

This article presents an improved fifth-order finite difference weighted essentially nonoscillatory (WENO) scheme to solve Hamilton-Jacobi equations. A new type of nonlinear weights is introduced with the construction of local smoothness indicators on each local stencil that are measured with the help of generalized undivided differences in L¹-norm. A novel global smoothness measurement is also constructed with the help of local measurements from its linear combination. Numerical experiments are conducted in one- and two-dimensions to demonstrate the performance enhancement, resolution power, numerical accuracy for the proposed scheme, and compared it with the classical WENO scheme.     

Thermal Degradation and Fire Behavior of High Performance Polymers

Abstract

High performance and high temperature polymers are a class of polymeric materials exhibiting high thermal stability and their resistance to fire makes them valuable assets for many applications. Those applications include as typical examples high temperature gas separation membranes, automotive and aerospace industry as well as the construction industry. The high performance polymers have been synthesized since the early 1960s, and have developed rapidly over the past few decades. Most high performance polymers comprise a highly aromatic backbone, linear chains, and strong inter-chain interactions. This review deals mostly with commercial polymeric materials. Studies regarding their thermal behavior, degradation mechanism and their reaction to fire have been synthetically combined in order to bring out potential insight concerning the effect of the thermal decomposition and thermal behavior on the fire properties of those polymers.     

Sequential Co-Sparse Factor Regression

In multivariate regression models, a sparse singular value decomposition of the regression component matrix is appealing for reducing dimensionality and facilitating interpretation. However, the recovery of such a decomposition remains very challenging, largely due to the simultaneous presence of orthogonality constraints and co-sparsity regularization. By delving into the underlying statistical data-generation mechanism, we reformulate the problem as a supervised co-sparse factor analysis, and develop an efficient computational procedure, named sequential factor extraction via co-sparse unit-rank estimation (SeCURE), that completely bypasses the orthogonality requirements. At each step, the problem reduces to a sparse multivariate regression with a unit-rank constraint. Nicely, each sequentially extracted sparse and unit-rank coefficient matrix automatically leads to co-sparsity in its pair of singular vectors. Each latent factor is thus a sparse linear combination of the predictors and may influence only a subset of responses. The proposed algorithm is guaranteed to converge, and it ensures efficient computation even with incomplete data and/or when enforcing exact orthogonality is desired. Our estimators enjoy the oracle properties asymptotically; a non-asymptotic error bound further reveals some interesting finite-sample behaviors of the estimators. The efficacy of SeCURE is demonstrated by simulation studies and two applications in genetics. Supplementary materials for this article are available online.     

Improved third‐order weighted essentially nonoscillatory scheme

A new third‐order WENO scheme is proposed to achieve the desired order of convergence at the critical points for scalar hyperbolic equations. A new reference smoothness indicator is introduced, which satisfies the sufficient condition on the weights for the third‐order convergence. Following the truncation error analysis, we have shown that the proposed scheme achieves the desired order accurate for smooth solutions with arbitrary number of vanishing derivatives if the parameter ε satisfies certain conditions. We have made a comparative study of the proposed scheme with the existing schemes such as WENO‐JS, WENO‐Z, and WENO‐N3 through different numerical examples. The result shows that the proposed scheme (WENO‐MN3) achieves better performance than these schemes.     

A Robust numerical approach for singularly perturbed time delayed parabolic partial differential equations

We consider the numerical solution of a initial boundary value problem with a time delay. The problem under consideration is singularly perturbed from the mathematical perspective. Assuming that the coefficients of the differential equation are smooth, we construct and analyze the finite difference method whose solutions converge pointwise at all points of the domain independently of the singular perturbation parameter. The method permits its extension to the case of adaptive meshes, which may be used to improve the solution. Numerical examples are presented to demonstrate the effectiveness of the method. The convergence obtained in practice satisfies the theoretical predictions.     

Third‐order WENO scheme with a new smoothness indicator

In this article, we have devised a new reference smoothness indicator for third‐order weighted essentially non‐oscillatory (WENO) scheme to achieve desired order of convergence at critical points. In the context of the weighted essentially non‐oscillatory scheme, reference smoothness indicator is constructed in such a way that it satisfies the sufficient condition on the weights for the third‐order convergence. The goal is to construct a reference smoothness indicator such that the resulted scheme have to achieve the required order of accuracy even if the first two derivatives vanish but not the third derivative. The construction of such reference smoothness indicator is not possible through a linear combination of local smoothness indicators only. We have proposed a reference smoothness indicator to be of the fourth order of accuracy on three‐point stencil that contains the linear combination of the first derivative information of the local and global stencils. The performance enhancement of the WENO scheme through this reference smoothness indicator is verified through the standard numerical experiments. Numerical results indicate that the new scheme provides better results in comparison with the earlier third‐order WENO schemes like WENO‐JS and WENO‐Z. Copyright © 2017 John Wiley & Sons, Ltd.     

Robust sparse phase retrieval made easy

In this short note we propose a simple two-stage sparse phase retrieval strategy that uses a near-optimal number of measurements, and is both computationally efficient and robust to measurement noise. In addition, the proposed strategy is fairly general, allowing for a large number of new measurement constructions and recovery algorithms to be designed with minimal effort.     

Thermal and electronic charge transport in bulk nanostructured Zr0.25Hf0.75NiSn composites with full-Heusler inclusions

Bulk Zr_0.25Hf₀₇₅NiSn half-Heusler (HH) nanocomposites containing various mole fractions of full-Heusler (FH) inclusions were prepared by solid state reaction of pre-synthesized HH alloy with elemental Ni at 1073 K. The microstructures of spark plasma sintered specimens of the HH/FH nanocomposites were investigated using transmission electron microscopy and their thermoelectric properties were measured from 300 K to 775 K. The formation of coherent FH inclusions into the HH matrix arises from solid-state Ni diffusion into vacant sites of the HH structure. HH(1–y)/FH(y) composites with mole fraction of FH inclusions below the percolation threshold, y∼0.2, show increased electrical conductivity, reduced Seebeck coefficient and increased total thermal conductivity arising from gradual increase in the carrier concentration for composites. A drastic reduction (∼55%) in κ_l was observed for the composite with y=0.6 and is attributed to enhanced phonon scattering due to mass fluctuations between FH and HH, and high density of HH/FH interfaces.     

Protein Allostery at Atomic Resolution

Protein allostery is a phenomenon involving the long range coupling between two distal sites in a protein. In order to elucidate allostery at atomic resoluion on the ligand-binding WW domain of the enzyme Pin1, multistate structures were calculated from exact nuclear Overhauser effect (eNOE). In its free form, the protein undergoes a microsecond exchange between two states, one of which is predisposed to interact with its parent catalytic domain. In presence of the positive allosteric ligand, the equilibrium between the two states is shifted towards domain–domain interaction, suggesting a population shift model. In contrast, the allostery-suppressing ligand decouples the side-chain arrangement at the inter-domain interface thereby reducing the inter-domain interaction. As such, this mechanism is an example of dynamic allostery. The presented distinct modes of action highlight the power of the interplay between dynamics and function in the biological activity of proteins.     

Stereoselective total synthesis of styryl-lactones: (+)-crassalactones B and C, (+)-howiionol A, (+)-tricinnamate, (+)-goniofufurone and (+)-dicinnamoyl goniofufurone

The total synthesis of (+)-crassalactone B, (+)-crassalactone C, (+)-howiionol A, (+)-tricinnamate, (+)-goniofufurone, and (+)-dicinnamoyl goniofufurone is achieved by a ‘chiron approach’ starting from diacetone d-glucose (DAG). Mitsunobu inversion, Wittig olefination and ring closing metatheses were used as key steps for (+)-howiionol A and (+)-tricinnamate. Meldrum’s acid was used for the synthesis of (+)-crassalactone C, (+)-goniofufurone, and (+)-dicinnamoyl goniofufurone. Yamaguchi esterification was used for (+)-crassalactone B, while a Grignard reaction followed by concomitant deallylation was first reported in the synthesis of (+)-dicinnamoyl goniofufurone.