Evolution of thermal properties from graphene to graphite

PublishedJournal ArticleWe report on the evolution of thermal properties from graphene to graphite as a function of layer thickness and temperature. The onset of the inter-layer compressional elastic constant C33 and the shear elastic constant C44 results in a large difference between the magnitudes and temperature dependencies of the specific heat and in-plane lattice thermal conductivity of bi-layer graphene (BLG) and single-layer graphene. The changes between BLG and few-layer graphene (FLG) decrease with increase in the number of layers. The cross-plane lattice thermal conductivity increases almost linearly with the number of layers in ultra-thin FLG. © 2014 AIP Publishing LLC.Taibah University, Madinah, Saudi Arabi

An Efficient Collocation Method for a Class of Boundary Value Problems Arising in Mathematical Physics and Geometry

We present a numerical method for a class of boundary value problems on the unit interval which feature a type of powerlaw nonlinearity. In order to numerically solve this type of nonlinear boundary value problems, we construct a kind of spectral collocation method. The spatial approximation is based on shifted Jacobi polynomials J(n)((alpha,beta))(r) with alpha,beta epsilon (-1, infinity), r epsilon (0,1) and n the polynomial degree. The shifted Jacobi-Gauss points are used as collocation nodes for the spectral method. After deriving the method for a rather general class of equations, we apply it to several specific examples. One natural example is a nonlinear boundary value problem related to the Yamabe problem which arises in mathematical physics and geometry. A number of specific numerical experiments demonstrate the accuracy and the efficiency of the spectral method. We discuss the extension of the method to account for more complicated forms of nonlinearity

Selecting Miners within Blockchain-based Systems Using Evolutionary Algorithms for Energy Optimisation

In this paper, we represent the problem of selecting miners within a blockchain-based system as a subset selection problem. We formulate the problem of minimising blockchain energy consumption as an optimisation problem with two conflicting objectives: energy consumption and trust. The proposed model is compared across different algorithms to demonstrate its performance.Comment: To appear in 2021 Genetic and Evolutionary Computation Conference Companion (GECCO '21 Companion), July 10--14, 2021, Lille, Franc

An Accurate Spectral Galerkin Method for Solving Multiterm Fractional Differential Equations

This paper reports a new formula expressing the Caputo fractional derivatives for any order of shifted generalized Jacobi polynomials of any degree in terms of shifted generalized Jacobi polynomials themselves. A direct solution technique is presented for solving multiterm fractional differential equations (FDEs) subject to nonhomogeneous initial conditions using spectral shifted generalized Jacobi Galerkin method. The homogeneous initial conditions are satisfied exactly by using a class of shifted generalized Jacobi polynomials as a polynomial basis of the truncated expansion for the approximate solution. The approximation of the spatial Caputo fractional order derivatives is expanded in terms of a class of shifted generalized Jacobi polynomials Jnα,−β(x) with x∈(0,1), and n is the polynomial degree. Several numerical examples with comparisons with the exact solutions are given to confirm the reliability of the proposed method for multiterm FDEs

Generalized Mixed Equilibria, Variational Inclusions, and Fixed Point Problems

We propose two iterative algorithms for finding a common element of the set of solutions of finite generalized mixed equilibrium problems, the set of solutions of finite variational inclusions for maximal monotone and inverse strong monotone mappings, and the set of common fixed points of infinite nonexpansive mappings and an asymptotically κ-strict pseudocontractive mapping in the intermediate sense in a real Hilbert space. We prove some strong and weak convergence theorems for the proposed iterative algorithms under suitable conditions

Oligodendrocyte pathology exceeds axonal pathology in white matter in human amyotrophic lateral sclerosis

Amyotrophic lateral sclerosis (ALS) is a neurodegenerative disease. The majority of cases are sporadic (sALS) while the most common inherited form is due to C9orf72 mutation (C9ALS). A high burden of inclusion pathology is seen in glia (including oligodendrocytes) in ALS, especially in C9ALS. Myelin basic protein (MBP) messenger RNA (mRNA) must be transported to oligodendrocyte processes for myelination, a possible vulnerability for normal function. TDP43 is found in pathological inclusions in ALS and is a component of mRNA transport granules. Thus, TDP43 aggregation could lead to MBP loss. Additionally, the hexanucleotide expansion of mutant C9ALS, binds hnRNPA2/B1, a protein essential for mRNA transport causing potential further impairment of hnRNPA2/B1 function, and thus myelination. Using immunohistochemistry p62 and TDP43 in human post mortem tissue, we found a high burden of glial inclusions in the prefrontal cortex, precentral gyrus and spinal cord in ALS, which was greater in C9ALS than sALS cases. Double staining demonstrated the majority of these inclusions were in oligodendrocytes. Using immunoblotting, we demonstrated reduced MBP protein levels relative to PLP (a myelin component that relies on protein not mRNA transport) and neurofilament protein (an axonal marker) in the spinal cord. This MBP loss was disproportionate to the level of PLP and axonal loss, suggesting that impaired mRNA transport may be partly responsible. Finally, we show that in C9ALS cases, the level of oligodendroglial inclusions correlates inversely with levels of hnRNPA2/B1 and the number of oligodendrocyte precursor cells. We conclude that there is considerable oligodendrocyte pathology in ALS, which at least partially reflects impairment of mRNA transport