A Finite Element Galerkin Method for a Unidimensional Single-Phase Nonlinear Stefan Problem with Dirichlet Boundary Conditions

Based on straightening the free boundary, an H¹-Galerkin methodis proposed and analysed for a single-phase nonlinear Stefanproblem with Dirichlet boundary conditions. Optimal H¹ estimatesfor continuous-time Galerkin approximations are derived.     

Evaluation of a novel nanocrystalline hydroxyapatite powder and a solid hydroxyapatite/Chitosan-Gelatin bioceramic for scaffold preparation used as a bone substitute material

Artificially fabricated hydroxyapatite (HAP) shows excellent biocompatibility with various kinds of cells and tissues which makes it an ideal candidate for a bone substitute material. In this study, hydroxyapatite nanoparticles have been prepared by using the wet chemical precipitation method using calcium nitrate tetra-hydrate [Ca(NO₃)₂.4H₂O] and di-ammonium hydrogen phosphate [(NH₄)₂ HPO₄] as precursors. The composite scaffolds have been prepared by a freeze-drying method with hydroxyapatite, chitosan, and gelatin which form a 3D network of interconnected pores. Glutaraldehyde solution has been used in the scaffolds to crosslink the amino groups (|NH₂) of gelatin with the aldehyde groups (|CHO) of chitosan. The X-ray diffraction (XRD) performed on different scaffolds indicates that the incorporation of a certain amount of hydroxyapatite has no influence on the chitosan/gelatin network and at the same time, the organic matrix does not affect the crystallinity of hydroxyapatite. Transmission electron microscope (TEM) images show the needle-like crystal structure of hydroxyapatite nanoparticle. Scanning Electron Microscope (SEM) analysis shows an interconnected porous network in the scaffold where HAP nanoparticles are found to be dispersed in the biopolymer matrix. Fourier transforms infrared spectroscopy (FTIR) confirms the presence of hydroxyl group (OH^-) , phosphate group (PO^3-₄) , carbonate group (CO^2-₃) , imine group (C=N), etc. TGA reveals the thermal stability of the scaffolds. The cytotoxicity of the scaffolds is examined qualitatively by VERO (animal cell) cell and quantitatively by MTTassay. The MTT-assay suggests keeping the weight percentage of glutaraldehyde solution lower than 0.2%. The result found from this study demonstrated that a proper bone replacing scaffold can be made up by controlling the amount of hydroxyapatite, gelatin, and chitosan which will be biocompatible, biodegradable, and biofriendly for any living organism.     

A Priori Error Estimates for a Single-Phase Quasilinear Stefan Problem in one Space Dimension

Fixing the free boundary with the help of a Landau-type transformation,a finite element Galerkin method is applied to a single-phasequasilinear Stefan problem in one space dimension. Optimal errorestimates both for semidiscrete and fully discrete Galerkinapproximations are derived.     

Energy in the Kantowski–Sachs space-time using teleparallel geometry

The purpose of this paper is to examine the energy content of the inflationary Universe described by Kantowski–Sachs space-time in quasilocal approach of teleparallel gravity and in the Hamiltonian structure of the teleparallel equivalent of general relativity. The teleparallel versions of field equations are also derived in such a space-time.     

Fixed Points of Mappings Satisfying a Weakly Contractive Type Condition

In this paper, we discuss a fixed point theorem for mappings derived by a pair of mappings satisfying weak(k, k/) contractive type condition on the tensor product spaces. Let X and Y be Banach spaces and T_1 : X γ Y → X and T_2: X γ Y → Y be two operators which satisfy weak(k, k/) contractive type condition. Using T_1 and T_2, we construct an operator T on X γ Y and show that T has a unique fixed point in a closed and bounded subset of X γ Y.We derive an iteration scheme converging to this unique fixed point of T. Conversely, using a weakly contractive mapping T, we construct a pair of mappings(T_1, T_2) satisfying weak(k, k/)contractive type condition on X γ Y and from this pair, we also obtain two self mappings S_1 and S_2 on X and Y respectively with unique fixed points.     

Distance signless Laplacian eigenvalues of graphs

Suppose that the vertex set of a graph G is V(G)=\{v\mathrm{1},v\mathrm{2},\mathrm{...},vn\}. The transmission Tr(vi) (or D_i) of vertex vi is defined to be the sum of distances from vi to all other vertices. Let Tr(G) be the n\times n diagonal matrix with its (i, i)-entry equal to {{\displaystyle Tr}}_G(vi). The distance signless Laplacian spectral radius of a connected graph G is the spectral radius of the distance signless Laplacian matrix of G, defined as L(G)=Tr(G)+D(G), where D(G) is the distance matrix of G. In this paper, we give a lower bound on the distance signless Laplacian spectral radius of graphs and characterize graphs for which these bounds are best possible. We obtain a lower bound on the second largest distance signless Laplacian eigenvalue of graphs. Moreover, we present lower bounds on the spread of distance signless Laplacian matrix of graphs and trees, and characterize extremal graphs.     

Nuclear multifragmentation: Basic concepts

We present a brief overview of nuclear multifragmentation reaction. Basic formalism of canonical thermodynamical model based on equilibrium statistical mechanics is described. This model is used to calculate basic observables of nuclear multifragmentation like mass distribution, fragment multiplicity, isotopic distribution and isoscaling. Extension of canonical thermodynamical model to a projectile fragmentation model is outlined. Application of the projectile fragmentation model for calculating average number of intermediate mass fragments and the average size of the largest cluster at different Z _bound, differential charge distribution and cross-section of neutron-rich nuclei of different projectile fragmentation reactions at different energies are described. Application of nuclear multifragmentation reaction in basic research as well as in other domains is outlined.     

A Priori Error Estimates in H1 and H2 Norms for Galerkin Approximations to a Single-Phase Nonlinear Stefan Problem in One Space Dimension

Optimal error estimates in H₁ and H₂ norms for continuous-timeGalerkin approximations of a single-phase nonlinear Stefan problemin one space dimension are derived.     

Probing of complete and incomplete fusion dynamics in heavy-ion collision

Three different types of experiments have been performed to explore the complete and incomplete fusion dynamics in heavy-ion collisions. In this respect, first experiment for the measurement of excitation functions of the evaporation residues produced in the ²⁰Ne + ¹⁶⁵Ho system at projectile energy ranges ≈2–8 MeV /nucleon has been done. Measured cumulative and direct cross-sections have been compared with the theoretical model code PACE-2, which takes into account only the complete fusion process. It has been observed that, incomplete fusion fraction is sensitively dependent on projectile energy and mass asymmetry between the projectile and the target systems. Second experiment for measuring the forward recoil range distributions of the evaporation residues produced in the ²⁰Ne + ¹⁶⁵Ho system at projectile energy ≈8 MeV /nucleon has been done. It has been observed that, some evaporation residues have shown additional peaks in the measured forwardrecoil range distributions at cumulative thicknesses relatively smaller than the expected range of the residues produced via complete fusion. The results indicate the occurrence of incomplete fusion involving the breakup of ²⁰Ne into ⁴He + ¹⁶O and /or ⁸Be + ¹²C followed by one of the fragments with target nucleus ¹⁶⁵Ho. Third experiment for the measurement of spin distribution of the evaporation residues produced in the ¹⁶O + ¹²⁴Sn system at projectile energy ≈6 MeV /nucleon, showed that the residues produced as incomplete fusion products associated with fast α and 2 α-emission channels observed in the forward cone, are found to be distinctly different from those of the residues produced as complete fusion products. The spin distribution of the evaporation residues also inferred that in incomplete fusion reaction channels input angular momentum (J ₀) increases with fusion incompleteness when compared to complete fusion reaction channels. Present observation clearly shows that the production of fast forward α-particles arises from relatively larger angular momentum in the entrance channel leading to peripheral collision.     

Collisionless stopping of electron current in an inhomogeneous electron magnetohydrodynamics plasma

A brief review of a recent work on a novel collisionless scheme for stopping electron current pulse in plasma is presented. This scheme relies on the inhomogeneity of the plasma medium. This mechanism can be used for heating an overdense regime of plasma where lasers cannot penetrate. The method can ensure efficient localized heating at a desired location. The suitability of the scheme to the frontline fast ignition laser fusion experiment has been illustrated.