New observations on scratch deformations of soda lime silica glass

In spite of the wealth of literature, the role of the scratching speed in affecting the material removal mechanism in soda lime silica (SLS) glass is yet to be comprehensively understood. Here we report the surface and sub‐surface deformation mechanisms of SLS glass scratched under three different normal loads of 5, 10 and 15 N at various speeds in the range of 100–1000 μm/s with a diamond indenter of ~ 200 μm tip radius. The results show that at any given applied normal load, the width, depth, wear volume of the scratch grooves and wear rate of the SLS glass decreased with an inverse power law dependence on the applied scratching speed. The surface damage also reduced with the increase in scratching speed. A new, simple model was developed to explain these observations. The significant contributions of the time of contact, the tensile stress behind the indenter and the shear stress active just underneath the indenter in governing the material removal mechanisms of the SLS glass were discussed.     

Magnetocaloric effect and multifunctional properties of Ni–Mn-based Heusler alloys

The studies of magnetocaloric properties, phase transitions, and phenomena related to magnetic heterogeneity in the vicinity of the martensitic transition (MT) in Ni–Mn–In and Ni–Mn–Ga off-stoichiometric Heusler alloys are summarized. The crystal structure, magnetocaloric effect (MCE), and magnetotransport properties were studied for the following alloys: Ni₅₀Mn_50−xIn_x, Ni_50−xCo_xMn₃₅In₁₅, Ni₅₀Mn_35−xCo_xIn₁₅, Ni₅₀Mn₃₅In₁₄Z (Z=Al, Ge), Ni₅₀Mn₃₅In_15−xSi_x, Ni_50−xCo_xMn_25+yGa_25−y, and Ni_50–xCo_xMn_32−yFeyGa₁₈. It was found that the magnetic entropy change, ΔS, associated with the inverse MCE in the vicinity of the temperature of the magneto-structural transition, TM, persists in a range of (125-5) J/(kg K) for a magnetic field change ΔH=5 T. The corresponding temperature varies with composition from 143 to 400 K. The MT in Ni₅₀Mn_50−xIn_x (x=13.5) results in a transition between two paramagnetic states. Associated with the paramagnetic austenite-paramagnetic martensite transition ΔS=24 J/(kg K) was detected for ΔH=5 T at T=350 K. The variation in composition of Ni₂MnGa can drastically change the magnetic state of the martensitic phase below and in the vicinity of TM. The presence of the martensitic phase with magnetic moment much smaller than that in the austenitic phase above TM leads to the large inverse MCE in the Ni₄₂Co₈Mn_32−yFeyGa₁₈ system. The adiabatic change of temperature (ΔT_ad) in the vicinity of TC and TM of Ni₅₀Mn₃₅In₁₅ and Ni₅₀Mn₃₅In₁₄Z (Z=Al, Ge) was found to be ΔT_ad=−2 K and 2 K for ΔH=1.8 T, respectively. It was observed that |ΔT_ad|≈1 K for ΔH=1 T for both types of transitions. The results on resistivity, magnetoresistance, Hall resistivity in some In-based alloys are discussed.     

The Finite Element Method on the Sierpinski Gasket

For certain classes of fractal differential equations on the Sierpinski gasket, built using the Kigami Laplacian, we describe how to approximate solutions using the finite element method based on piecewise harmonic or piecewise biharmonic splines. We give theoretical error estimates, and compare these with experimental data obtained using a computer implementation of the method (available at the web site http://mathlab.cit.cornell.edu/\sim gibbons). We also explain some interesting structure concerning the spectrum of the Laplacian that became apparent from the experimental data. March 29, 2000. Date revised: March 6, 2001. Date accepted: March 21, 2001.     

Biochemical Characterization and In Vitro Digestibility of Protein Isolates from Hemp (Cannabis sativa L.) By-Products for Salmonid Feed Applications

Hemp (Cannabis sativa L.) processing by-products (hemp cake and hemp seed hulls) were studied for their protein content, extraction of protein isolates (PIs), and their in vitro protein digestibility (IVPD). Crude protein contents of hemp cake and hemp seed hulls were 30.4% and 8.6%, respectively, calculated based on generalized N-to-P conversion factor (N × 5.37). Extraction efficiency of PIs from defatted biomass ranged from 56.0 to 67.7% with alkaline extraction (0.1 M NaOH) followed by isoelectric precipitation (1.0 M HCl). Nitrogen analysis suggested that the total protein contents of PIs extracted using three different alkaline conditions (0.5 M, 0.1 M, and pH 10.0 with NaOH) were >69.7%. The hemp by-product PIs contained all essential amino acids (EAAs) required for fish with leucine, valine, and phenylalanine belonging to the five dominant amino acids. Overall, glutamate was the dominant non-EAA followed by aspartate. Coomassie staining of an SDS-PAGE gel revealed strong presence of the storage protein edestin. High IVPD of >88% was observed for PIs extracted from hemp seeds and by-products when evaluated using a two-phase in vitro gastric/pancreatic protein digestibility assay. PIs extracted from by-products were further tested for their antioxidant activities. The tested PIs showed dose-dependent DPPH radical scavenging activity and possessed strong ORAC values > 650 μM TE/g.     

On degrees of maps between Grassmannians

Let G_n,k denote the oriented grassmann manifold of orientedk-planes in ℝⁿ. It is shown that for any continuous mapf: G_n,k → G_n,k, dim G_n,k = dim G_m,l = l(m −l), the Brouwer’s degree is zero, providedl > 1,n ≠ m. Similar results for continuous mapsg: ℂG_m,l → ℂG_n,k,h: ℍG_m,l → ℍG_n,k, 1 ≤ l < k ≤ n/2, k(n — k) = l(m — l) are also obtained.     

On Some Tests of the Covariance Matrix Under General Conditions

We consider the problem of testing the hypothesis about the covariance matrix of random vectors under the assumptions that the underlying distributions are nonnormal and the sample size is moderate. The asymptotic expansions of the null distributions are obtained up to n ^−1/2. It is found that in most cases the null statistics are distributed as a mixture of independent chi-square random variables with degree of freedom one (up to n ^−1/2) and the coefficients of the mixtures are functions of the fourth cumulants of the original random variables. We also provide a general method to approximate such distributions based on a normalization transformation.     

A Class of Integrable and Nonintegrable Mappings and their Dynamics

We analyse a class of mappings which by construction do not belong to the QRT family. We show that some of the members of this class have invariants of high degree. A new linearisable mapping is also identified. A mapping which possesses confined singularities while having nonzero algebraic entropy is presented. Its dynamics are studied in detail and shown to be related intimately to the Fibonacci recurrence.      

Special functions as solutions to discrete Painlevé equations

We present results on special solutions of discrete Painlevé equations. These solutions exist only when one constraint among the parameters of the equation is satisfied and are obtained through the solutions of linear second-order (discrete) equations. These linear equations define the discrete analogues of special functions.     

2-Nitrobenzaldehyde Thiocarbohydrazone Assisted Precise Extraction Spectrophotometric Method for the Determination of Ruthenium(III) in Alloy and Catalysts

A simple, rapid, selective, sensitive and reliable extractive spectrophotometric method was developed for the determination of ruthenium(III) using 2-nitrobenzaldehyde thiocarbohydrazone (2-NBATCH) as a chromogenic chelating ligand. The ruthenium(III)?2-NBATCH complex is formed in aqueous acetic acid media (0.7 M) containing an organic solvent after 5 min heating on a water bath. The red colored complex is extracted into 1,2-dichloroethane and absorbance is measured at 445 nm against reagent blank. The Beer’s law is obeyed within 1?6 g/mL of ruthenium(III), the optimum concentration range was 2?5 g/mL of ruthenium(III) evaluated by Ringbom’s plot. Molar absorptivity and Sandell’s sensitivity of complex were 1.41 × 10⁴ L/mol/cm and 0.0075 μg/cm², respectively. The stoichiometry of complex was 1: 3 established from Job’s method of continuous variation, molar ratio method and logarithmic slope method. The proposed method was applied for determination of ruthenium(III) in binary and ternary, synthetic mixtures corresponding to fission product elements alloy and ruthenium(III) catalysts.     

Microstructure of polycarbonate seen by positrons as an in-situ probe

Positron Annihilation Lifetime Spectroscopy (PALS) is used to probe the micro-structural changes in the polymer polycarbonate in terms of the changes in free volume hole size and their content as a function of temperature. The measured spectra are best fitted to three lifetime component analysis. The average hole size in the amorphous regions is determined from the measured Ortho Positronium (O-Ps) lifetime ₃ by following the treatment of Nakanishi et al. On the other hand, information about defects in the crystalline regions is revealed by trapped positrons lifetime ₂. In this polymer the average hole radius varies from 2.71 Å to 2.77 Å. The present study indicates that this polymer has a glass transition temperature of 152°C. Further, we have calculated the trapping rates in the ordered and disordered regions of the polymer based on Goldanskii's kinetic equations and an attempt is made for the first time to estimate the activation energy in the amorphous and crystalline regions separately.