Ground state of lutetium dimer by density functional methods

Bond distances, vibrational frequencies and dissociation energies for the ground state of Lu-2 were studied by density functional methods B3LYP, B3PW91, BLYP, BHLYP, BP86, B3P86, MPW1PW91, PBE1PBE and SVWN with CEP-121G and SDD basis sets. Singlet state is predicted to be the most stable. CEP-121G has a better overall performance than SDD. At CEP-121G basis set, all density functional methods used in this study perform well in reproducing the spectroscopic constants.

Distribution of the Demmel Condition Number of Wishart Matrices

This paper studies the Demmel condition number of Wishart matrices, a quantity which has numerous applications to wireless communications, such as adaptive switching between beamforming and diversity coding, link adaptation, and spectrum sensing. For complex Wishart matrices, we give an exact analytical expression for the probability density function (p.d.f.) of the Demmel condition number, and also derive simplified expressions for the high tail regime. These results indicate that the condition of complex Wishart matrices is dominantly decided by the difference between the matrix dimension and degree of freedom (DoF), i.e., the probability of drawing a highly ill conditioned matrix decreases considerably when the difference between the matrix dimension and DoF increases. We further investigate real Wishart matrices, and derive new expressions for the p.d.f. of the smallest eigenvalue, when the difference between the matrix dimension and DoF is odd. Based on these results, we succeed to obtain an exact p.d.f. expression for the Demmel condition number, and simplified expressions for the high tail regime.

Aspects géométriques et intégrables des modèles de matrices aléatoires

Travail réalisé en cotutelle avec l'université Paris-Diderot et le Commissariat à l'Energie Atomique sous la direction de John Harnad et Bertrand Eynard.

On some Density Theorems in Number Theory and Group Theory

Gowers, dans son article sur les matrices quasi-aléatoires, étudie la question, posée par Babai et Sos, de l'existence d'une constante $c>0$ telle que tout groupe fini possède un sous-ensemble sans produit de taille supérieure ou égale a $c|G|$. En prouvant que, pour tout nombre premier $p$ assez grand, le groupe $PSL_2(\mathbb{F}_p)$ (d'ordre noté $n$) ne posséde aucun sous-ensemble sans produit de taille $c n^{8/9}$, il y répond par la négative. Nous allons considérer le probléme dans le cas des groupes compacts finis, et plus particuliérement des groupes profinis $SL_k(\mathbb{Z}_p)$ et $Sp_{2k}(\mathbb{Z}_p)$. La premiére partie de cette thése est dédiée à l'obtention de bornes inférieures et supérieures exponentielles pour la mesure suprémale des ensembles sans produit. La preuve nécessite d'établir préalablement une borne inférieure sur la dimension des représentations non-triviales des groupes finis $SL_k(\mathbb{Z}/(p^n\mathbb{Z}))$ et $Sp_{2k}(\mathbb{Z}/(p^n\mathbb{Z}))$. Notre théoréme prolonge le travail de Landazuri et Seitz, qui considérent le degré minimal des représentations pour les groupes de Chevalley sur les corps finis, tout en offrant une preuve plus simple que la leur. La seconde partie de la thése à trait à la théorie algébrique des nombres. Un polynome monogéne $f$ est un polynome unitaire irréductible à coefficients entiers qui endengre un corps de nombres monogéne. Pour un nombre premier $q$ donné, nous allons montrer, en utilisant le théoréme de densité de Tchebotariov, que la densité des nombres premiers $p$ tels que $t^q -p$ soit monogéne est supérieure ou égale à $(q-1)/q$. Nous allons également démontrer que, quand $q=3$, la densité des nombres premiers $p$ tels que $\mathbb{Q}(\sqrt[3]{p})$ soit non monogéne est supérieure ou égale à $1/9$.

Decomposition of spectral density in individual eigenvalue contributions

The eigenvalue densities of two random matrix ensembles, the Wigner Gaussian matrices and the Wishart covariant matrices, are decomposed in the contributions of each individual eigenvalue distribution. It is shown that the fluctuations of all eigenvalues, for medium matrix sizes, are described with a good precision by nearly normal distributions.

Density profiles in the raise and peel model with and without a wall; physics and combinatorics

We consider the raise and peel model of a one-dimensional fluctuating interface in the presence of an attractive wall. The model can also describe a pair annihilation process in disordered unquenched media with a source at one end of the system. For the stationary states, several density profiles are studied using Monte Carlo simulations. We point out a deep connection between some profiles seen in the presence of the wall and in its absence. Our results are discussed in the context of conformal invariance ( c = 0 theory). We discover some unexpected values for the critical exponents, which are obtained using combinatorial methods. We have solved known ( Pascal`s hexagon) and new (split-hexagon) bilinear recurrence relations. The solutions of these equations are interesting in their own right since they give information on certain classes of alternating sign matrices.

Characterization of high density polyethylene (HDPE) reinforced with banana peel fibers

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Insights into the swelling process and drug release mechanisms from cross-linked pectin/high amylose starch matrices

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

PMMA-CNT matrices for vacuum electronic, biosensing and energy applications

Carbon nanotubes (CNTs) are interesting materials with extraordinary properties for various applications. Here, vertically-aligned multiwalled CNTs (VA-MWCNTs) are grown by our dual radio frequency plasma enhanced chemical vapor deposition (PECVD). After optimizing the synthesis processes, these VA-MWCNTs were fabricated in to a series of devices for applications in vacuum electronics, glucose biosensors, glucose biofuel cells, and supercapacitors In particular, we have created the so-called PMMA-CNT matrices (opened-tip CNTs embedded in poly-methyl methacrylate) that are promising components in a novel energy sensing, generation and storage (SGS) system that integrate glucose biosensors, biofuel cells, and supercapacitors. The content of this thesis work is described as follows: 1. We have first optimized the synthesis of VA-MWCNTs by our PECVD technique. The effects of CH4 flow rate and growth duration on the lengths of these CNTs were studied. 2. We have characterized these VA-MWCNTs for electron field emission. We noticed that as grown CNTs suffers from high emission threshold, poor emission density and poor long-term stability. We attempted a series of experiments to understand ways to overcome these problems. First, we decrease the screening effects on VA-MWCNTs by creating arrays of self-assembled CNT bundles that are catalyst-free and opened tips. These bundles are found to enhance the field emission stability and emission density. Subsequently, we have created PMMA-CNT matrices that are excellent electron field emitters with an emission threshold field of more than two-fold lower than that of the as-grown sample. Furthermore, no significant emission degradation was observed after a continuous emission test of 40 hours (versus much shorter tests in reported literatures). Based on the new understanding we learnt from the PMMA-CNT matrices, we further created PMMA-STO-CNT matrices by embedding opened-tip VA-MWCNTs that are coated with strontium titanate (SrTiO3) with PMMA. We found that the PMMA-STO-CNT matrices have all the desired properties of the PMMA-CNT matrices. Furthermore, PMMA-STO-CNT matrices offer much lower emission threshold field, about five-fold lower than that of as grown VA-MWCNTs. The new understandings we obtained are important for practical application of VA-MWCNTs in field emission devices. 3. Subsequently, we have functionalized PMMA-CNT matrices for glucose biosensing. Our biosensor was developed by immobilized glucose oxidase (GOχ) on the opened-tip CNTs exposed on the matrices. The durability, stability and sensitivity of the biosensor were studied. In order to understand the performance of miniaturized glucose biosensors, we have then investigated the effect of working electrode area on the sensitivity and current level of our biosensors. 4. Next, functionalized PMMA-CNT matrices were utilized for energy generation and storage. We found that PMMA-CNT matrices are promising component in glucose/O2 biofuel cells (BFCs) for energy generation. The construction of these BFCs and the effect of the electrode area on the power density of these BFCs were investigated. Then, we have attempted to use PMMA-CNT matrices as supercapacitors for energy storage devices. The performance of these supercapacitors and ways to enhance their performance are discussed. 5. Finally, we further evaluated the concept of energy SGS system that integrated glucose biosensors, biofuel cells, and supercapacitors. This SGS system may be implantable to monitor and control the blood glucose level in our body.

Statistical physics of low density parity check error correcting codes

We study the performance of Low Density Parity Check (LDPC) error-correcting codes using the methods of statistical physics. LDPC codes are based on the generation of codewords using Boolean sums of the original message bits by employing two randomly-constructed sparse matrices. These codes can be mapped onto Ising spin models and studied using common methods of statistical physics. We examine various regular constructions and obtain insight into their theoretical and practical limitations. We also briefly report on results obtained for irregular code constructions, for codes with non-binary alphabet, and on how a finite system size effects the error probability.

Spectra of modular and small-world matrices

We compute spectra of symmetric random matrices describing graphs with general modular structure and arbitrary inter- and intra-module degree distributions, subject only to the constraint of finite mean connectivities. We also evaluate spectra of a certain class of small-world matrices generated from random graphs by introducing shortcuts via additional random connectivity components. Both adjacency matrices and the associated graph Laplacians are investigated. For the Laplacians, we find Lifshitz-type singular behaviour of the spectral density in a localized region of small |?| values. In the case of modular networks, we can identify contributions of local densities of state from individual modules. For small-world networks, we find that the introduction of short cuts can lead to the creation of satellite bands outside the central band of extended states, exhibiting only localized states in the band gaps. Results for the ensemble in the thermodynamic limit are in excellent agreement with those obtained via a cavity approach for large finite single instances, and with direct diagonalization results.

Precipitation casting of drug-loaded microporous PCL matrices:incorporation of progesterone by co-dissolution

Microporous, poly(ε-caprolactone) (PCL) matrices were loaded with progesterone by precipitation casting using co-solutions of PCL and progesterone in acetone. Progesterone loadings up to 32% w/w were readily achieved by increasing the drug content of the starting PCL solution. The kinetics of steroid release in PBS at 37°C over 10 days could be described effectively by a diffusional release model although the Korsmeyer-Peppas model indicated the involvement of multiple release phenomena. The diffusion rate constant (D) increased from 8 to 24 μg/mg matrix/day0.5 as the drug loading increased from 3.6 to 12.4% w/w. A total cumulative release of 75%-95% indicates the high efficiency of steroid delivery. Increasing the matrix density from 0.22 to 0.39 g/cm3, by increasing the starting PCL solution concentration, was less effective in changing drug release kinetics. Retention of anti-proliferative activity of released steroid was confirmed using cultures of breast cancer epithelial (MCF-7) cells. Progesterone released from PCL matrices into PBS at 37°C over 14 days retarded the growth of MCF-7 cells by a factor of at least 3.5 compared with progesterone-free controls. These findings recommend further investigation of precipitation-cast PCL matrices for delivery of bioactive molecules such as anti-proliferative agents from implanted, inserted or topical devices.