Determinantal point processes in the plane from products of random matrices

We show that the density of eigenvalues for three classes of random matrix ensembles is determinantal. First we derive the density of eigenvalues of product of k independent n x n matrices with i.i.d. complex Gaussian entries with a few of matrices being inverted. In second example we calculate the same for (compatible) product of rectangular matrices with i.i.d. Gaussian entries and in last example we calculate for product of independent truncated unitary random matrices. We derive exact expressions for limiting expected empirical spectral distributions of above mentioned ensembles.

Combined Effect of Cryogel Matrix and Temperature-Reversible Soluble-Insoluble Polymer for the Development of in Vitro Human Liver Tissue

Hepatic cell culture on a three-dimensional (3D) matrix or as a hepatosphere appears to be a promising in vitro biomimetic system for liver tissue engineering applications. In this study, we have combined the concept of a 3D scaffold and a spheroid culture to develop an in vitro model to engineer liver tissue for drug screening. We have evaluated the potential of poly(ethylene glycol)-alginate-gelatin (PAG) cryogel matrix for in vitro culture of human liver cell lines. The synthesized cryogel matrix has a flow rate of 7 mL/min and water uptake capacity of 94% that enables easy nutrient transportation in the in vitro cell culture. Youngs modulus of 2.4 kPa and viscoelastic property determine the soft and elastic nature of synthesized cryogel. Biocompatibility of PAG cryogel was evaluated through MTT assay of HepG2 and Huh-7 cells on matrices. The proliferation and functionality of the liver cells were enhanced by culturing hepatic cells as spheroids (hepatospheres) on the PAG cryogel using temperature-reversible soluble-insoluble polymer, poly(N-isopropylacrylamide) (PNIPAAm). Pore size of the cryogel above 100 mu m modulated spheroid size that can prevent hypoxia condition within the spheroid culture. Both the hepatic cells have shown a significant difference (P < 0.05) in terms of cell number and functionality when cultured with PNIPAAm. After 10 days of culture using 0.05% PNIPAAm, the cell number increased by 11- and 7-fold in case of HepG2 and Huh-7 cells, respectively. Similarly, after 10 days of hepatic spheroids culture on PAG cryogel, the albumin production, urea secretion, and CYP450 activity were significantly higher in case of culture with PNIPAAm. The developed tissue mass on the PAG cryogel in the presence of PNIPAAm possess polarity, which was confirmed using F-actin staining and by presence of intercellular bile canalicular lumen. The developed cryogel matrix supports liver cells proliferation and functionality and therefore can be used for in vitro and in vivo drug testing.

Efficient density matrix renormalization group algorithm to study Y junctions with integer and half-integer spin

An efficient density matrix renormalization group (DMRG) algorithm is presented and applied to Y junctions, systems with three arms of n sites that meet at a central site. The accuracy is comparable to DMRG of chains. As in chains, new sites are always bonded to the most recently added sites and the superblock Hamiltonian contains only new or once renormalized operators. Junctions of up to N = 3n + 1 approximate to 500 sites are studied with antiferromagnetic (AF) Heisenberg exchange J between nearest-neighbor spins S or electron transfer t between nearest neighbors in half-filled Hubbard models. Exchange or electron transfer is exclusively between sites in two sublattices with N-A not equal N-B. The ground state (GS) and spin densities rho(r) = < S-r(z)> at site r are quite different for junctions with S = 1/2, 1, 3/2, and 2. The GS has finite total spin S-G = 2S(S) for even (odd) N and for M-G = S-G in the S-G spin manifold, rho(r) > 0(< 0) at sites of the larger (smaller) sublattice. S = 1/2 junctions have delocalized states and decreasing spin densities with increasing N. S = 1 junctions have four localized S-z = 1/2 states at the end of each arm and centered on the junction, consistent with localized states in S = 1 chains with finite Haldane gap. The GS of S = 3/2 or 2 junctions of up to 500 spins is a spin density wave with increased amplitude at the ends of arms or near the junction. Quantum fluctuations completely suppress AF order in S = 1/2 or 1 junctions, as well as in half-filled Hubbard junctions, but reduce rather than suppress AF order in S = 3/2 or 2 junctions.

Non-covalent C-Cl center dot center dot center dot pi interaction in acetylene-carbon tetrachloride adducts: Matrix isolation infrared and ab initio computational studies

Non-covalent halogen-bonding interactions between n cloud of acetylene (C2H2) and chlorine atom of carbon tetrachloride (CCl4) have been investigated using matrix isolation infrared spectroscopy and quantum chemical computations. The structure and the energies of the 1:1 C2H2-CCl4 adducts were computed at the B3LYP, MP2 and M05-2X levels of theory using 6-311++G(d,p) basis set. The computations indicated two minima for the 1:1 C2H2-CCl4 adducts; with the C-Cl center dot center dot center dot pi adduct being the global minimum, where pi cloud of C2H2 is the electron donor. The second minimum corresponded to a C-H...Cl adduct, in which C2H2 is the proton donor. The interaction energies for the adducts A and B were found to be nearly identical. Experimentally, both C-Cl center dot center dot center dot pi and C-H center dot center dot center dot Cl adducts were generated in Ar and N2 matrixes and characterized using infrared spectroscopy. This is the first report on halogen bonded adduct, stabilized through C-Cl center dot center dot center dot pi interaction being identified at low temperatures using matrix isolation infrared spectroscopy. Atoms in Molecules (AIM) and Natural Bond Orbital (NBO) analyses were performed to support the experimental results. The structures of 2:1 ((C2H2)(2)-CCl4) and 1:2 (C2H2-(CCl4)(2)) multimers and their identification in the low temperature matrixes were also discussed. (C) 2015 Elsevier B.V. All rights reserved.

Regulation of Growth, Cell Shape, Cell Division, and Gene Expression by Second Messengers (p)ppGpp and Cyclic Di-GMP in Mycobacterium smegmatis

The alarmone (p)ppGpp regulates transcription, translation, replication, virulence, lipid synthesis, antibiotic sensitivity, biofilm formation, and other functions in bacteria. Signaling nucleotide cyclic di-GMP (c-di-GMP) regulates biofilm formation, motility, virulence, the cell cycle, and other functions. In Mycobacterium smegmatis, both (p) ppGpp and c-di-GMP are synthesized and degraded by bifunctional proteins Rel(Msm) and DcpA, encoded by rel(Msm) and dcpA genes, respectively. We have previously shown that the Delta rel(Msm) and Delta dcpA knockout strains are antibiotic resistant and defective in biofilm formation, show altered cell surface properties, and have reduced levels of glycopeptidolipids and polar lipids in their cell wall (K. R. Gupta, S. Kasetty, and D. Chatterji, Appl Environ Microbiol 81:2571-2578, 2015, http://dx.doi.org/10.1128/AEM.03999-14). In this work, we have explored the phenotypes that are affected by both (p) ppGpp and c-di-GMP in mycobacteria. We have shown that both (p) ppGpp and c-di-GMP are needed to maintain the proper growth rate under stress conditions such as carbon deprivation and cold shock. Scanning electron microscopy showed that low levels of these second messengers result in elongated cells, while high levels reduce the cell length and embed the cells in a biofilm-like matrix. Fluorescence microscopy revealed that the elongated Delta rel(Msm) and Delta dcpA cells are multinucleate, while transmission electron microscopy showed that the elongated cells are multiseptate. Gene expression analysis also showed that genes belonging to functional categories such as virulence, detoxification, lipid metabolism, and cell-wall-related processes were differentially expressed. Our results suggests that both (p) ppGpp and c-di-GMP affect some common phenotypes in M. smegmatis, thus raising a possibility of cross talk between these two second messengers in mycobacteria. IMPORTANCE Our work has expanded the horizon of (p) ppGpp and c-di-GMP signaling in Gram-positive bacteria. We have come across a novel observation that M. smegmatis needs (p) ppGpp and c-di-GMP for cold tolerance. We had previously shown that the Delta rel(Msm) and Delta dcpA strains are defective in biofilm formation. In this work, the overproduction of (p) ppGpp and c-di-GMP encased M. smegmatis in a biofilm-like matrix, which shows that both (p) ppGpp and c-di-GMP are needed for biofilm formation. The regulation of cell length and cell division by (p) ppGpp was known in mycobacteria, but our work shows that c-di-GMP also affects the cell size and cell division in mycobacteria. This is perhaps the first report of c-di-GMP regulating cell division in mycobacteria.

Surface amorphous and crystalline microstructure by alloying zirconium using Nd : YAG pulsed laser

A novel composite coating was synthesized by laser alloying of zirconium nanoparticles on an austenite stainless steel surface using a pulsed Nd:YAG laser. The coating contained duplex microstructures comprising an amorphous phase and an austenitic matrix. A discontinuous zirconium-containing region formed at a depth of 16 mum below the surface. The amorphous phase was present in the zirconium-rich region, with the composition of zirconium ranging from 7.8 to 14.5 at. pet. The formation of the amorphous phase was attributed to the zirconium addition. The hardness, corrosion, and wear-corrosion resistance of the irradiated coating were evidently enhanced compared to those of the stainless steel.

Size-dependent inelastic behavior of particle-reinforced metal-matrix composites

The strengthening behavior of particle-reinforced metal-matrix composites (MMCp) is primarily attributed to the dislocation strengthening effect and the load-transfer effect. To account for these two effects in a unified way, a new hybrid approach is developed in this paper by incorporating the geometrically necessary dislocation strengthening effect into the incremental micromechanical scheme. By making use of this hybrid approach, the particle-size-dependent inelastic deformation behavior of MMCp is given. Some comparisons with the available experimental results demonstrate that the present approach is satisfactory.

An Amino Acid Substitution Matrix for Protein Conformation Identification

Amino acid substitution matrices play an essential role in protein sequence alignment, a fundamental task in bioinformatics. Most widely used matrices, such as PAM matrices derived from homologous sequences and BLOSUM matrices derived from aligned segments of PROSITE, did not integrate conformation information in their construction. There are a few structure-based matrices, which are derived from limited data of structure alignment. Using databases PDB_SELECT and DSSP, we create a database of sequence-conformation blocks which explicitly represent sequence-structure relationship. Members in a block are identical in conformation and are highly similar in sequence. From this block database, we derive a conformation-specific amino acid substitution matrix CBSM60. The matrix shows an improved performance in conformational segment search and homolog detection.

Flow Stress of Biomorphous Metal-Matrix Composites

For metal-matrix composites (MMCs), interfacial debonding between the ductile matrix and the reinforcing hard inclusions is an important failure mode. A fundamental approach to improving the properties of MMCs is to optimize their microstructure to achieve maximum strength and toughness. Here, we investigate the flow stress of a MMC with a nanoscale microstructure similar to that of bone. Such a 'biomorphous' MMC would be made of staggered hard and slender nanoparticles embedded in a ductile matrix. We show that the large aspect ratio and the nanometer size of inclusions in the biomorphous MMC lead to significantly improved properties with increased tolerance of interfacial damage. In this case, the partially debonded inclusions continue to carry mechanical load transferred via longitudinal shearing of the matrix material between neighboring inclusions. The larger the inclusion aspect ratio, the larger is the flow stress and work hardening rate for the composite. Increasing the volume concentration of inclusion also makes the biomorphous MMC more tolerant of interfacial damage.

Material response and failure mechanism of unidirectional metal matrix composites under impulsive shear loading

The material response and failure mechanism of unidirectional metal matrix composite under impulsive shear loading are investigated in this paper. Both experimental and analytical studies were performed. The shear strength of unidirectional C-f/A356.0 composite and A356.0 aluminum alloy at high strain rate were measured with a modified split Hopkinson torsional bar technique. The results indicated that the carbon fibers did not improve the shear strength of aluminum matrix if the fiber orientation aligned with the shear loading axis. The microscopic inspection of the fractured surface showed a multi-scale zigzag feature which implied a complicated shear failure mechanism in the composite. In addition to testing, the micromechanical stress field in the composite was analyzed by the generalized Eshelby equivalent method (GEEM). The influence of cracking in matrix on the micromechanical stress field was investigated as well. The results showed that the stress distribution in the composite is quite nonhomogeneous and very high shear stress concentrations are found in some regions in the matrix. The high shear stress concentration in the matrix induces tensile cracking at 45 degrees to the shear direction. This in turn aggravates the stress concentration at the fiber/matrix interface and finally leads to a catastrophic failure in the composite. From the correlation between the analysis and experimental results, the shear failure mechanism of unidirectional C-f/A356.0 composite can be elucidated qualitatively.

Enhanced Plasticity of Zr-Based Bulk Metallic Glass Matrix Composite with Ductile Reinforcement

A composite material containing uniformly distributed micrometer-sized Nb particles in a Zr-based amorphous matrix was prepared by suction cast. The resulting material exhibits high fractured strength over 1550 MPa and enhanced plastic strain of about 29.7% before failure in uniaxial compression test at room temperature. Studies of the serrations on the stress-strain curves and the shear bands on the fractured samples reveal that the amplitude of the stress drop of each serration step corresponds to the extent of the propagation of a single shear band through the materials. The composite exhibits more serration steps and smaller amplitude of stress drop due to the pinning of shear band propagation by ductile Nb particles.

Formation, Thermal Stability and Deformation Behavior of Graphite-Flakes Reinforced Cu-based Bulk Metallic Glass Matrix Composites

Graphite-flake reinforced Cu47Ti34Zr11 Ni-8 bulk metallic glass matrix composite was fabricated by water-cooled copper mould cast. Most of the graphite flakes still keep unreacted and distribute uniformly in the amorphous matrix except that some reactive wetting occurs by the formation of TiC particles around the flakes. It reveals that the presence of graphite flakes does not affect the onset of the glass transition temperature, crystallization reaction and liquidus of the metallic glass. The resulting material shows obvious serrated flow and higher fracture strength under room temperature compressive load, comparing with the monolithic bulk metallic glass (BMG). Three types of interaction between the shear bands and graphite flakes, namely, shear band termination, shear bands branching and new shear bands formation near the graphite flakes can be observed by quasi-static uniaxial compression test and bonded interface technique through Vickers indentation.

A new model for the energy release rate of fibre/matrix interfacial fracture

On the basis of the well-known shear-lag analysis of fibre/matrix interface stresses and the assumption of identical axial strains in the fibre and matrix, a new model for predicting the energy release rate of interfacial fracture of the fibre pull-out test model is attempted. The expressions for stresses in the fibre, matrix and interface are derived. The formula for interfacial debonding energy release rate is given. Numerical calculations are conducted and the results obtained are compared with those of the existing models.

Dynamic properties and asymmetry of tension and compression of metal matrix composites under impact loading

The mechanical behaviors of 2124, Al-5Cu, Al-Li and 6061 alloys reinforced by silicon carbide particulates, together with 15%SiCw/6061 alloy, were studied under the quasi-static and impact loading conditions, using the split Hopkinson tension/compression bars and Instron universal testing machine. The effect of strain rate on the ultra tensile strength (UTS), the hardening modulus and the failure strain was investigated. At the same time, the SEM observations of dynamic fracture surfaces of various MMC materials showed some distinguished microstructures and patterns. Some new characteristics of asymmetry of mechanical behaviors of MMCs under tension and compression loading were also presented and explained in details, and they could be considered as marks to indicate, to some degree, the mechanism of controlling damage and failure of MMCs under impact loading. The development of new constitutive laws about MMCs under impact loading should benefit from these experimental results and theoretical analysis.

Effect of Particle Size on the Formation of Adiabatic Shear Band In Particle Reinforced Metal Matrix Composites

In this paper, the effect of particle size on the formation of adiabatic shear band in 2024 All matrix composites reinforced with 15% volume fraction of 3.5, 10 and 20 mum SiC particles was investigated by making use of split Hopkinson pressure bar (SHPB). The results have demonstrated that the onset of adiabatic shear banding in the composites strongly depends on the particle size and adiabatic shear banding is more readily observed in the composite reinforced with small particles than that in the composite with large particles. This size dependency phenomenon can be characterized by the strain gradient effect. Instability analysis reveals that high strain gradient is a strong driving force for the formation of adiabatic shear banding in particle reinforced metal matrix composites (MMCp).