Analytic perturbation theory for bound states in the transfer matrix spectrum of weakly correlated lattice ferromagnetic spin systems

We consider general d-dimensional lattice ferromagnetic spin systems with nearest neighbor interactions in the high temperature region ('beta' << 1). Each model is characterized by a single site apriori spin distribution taken to be even. We also take the parameter 'alfa' = ('S POT.4') - 3 '(S POT.2') POT.2' > 0, i.e. in the region which we call Gaussian subjugation, where ('S POT.K') denotes the kth moment of the apriori distribution. Associated with the model is a lattice quantum field theory known to contain a particle of asymptotic mass -ln 'beta' and a bound state below the two-particle threshold. We develop a 'beta' analytic perturbation theory for the binding energy of this bound state. As a key ingredient in obtaining our result we show that the Fourier transform of the two-point function is a meromorphic function, with a simple pole, in a suitable complex spectral parameter and the coefficients of its Laurent expansion are analytic in 'beta'.

Application of H-infinity Theory to a 6 DOF Flight Simulator Motion Base

The purpose of this study is to apply inverse dynamics control for a six degree of freedom flight simulator motion system. Imperfect compensation of the inverse dynamic control is intentionally introduced in order to simplify the implementation of this approach. The control strategy is applied in the outer loop of the inverse dynamic control to counteract the effects of imperfect compensation. The control strategy is designed using H-infinity theory. Forward and inverse kinematics and full dynamic model of a six degrees of freedom motion base driven by electromechanical actuators are briefly presented. Describing function, acceleration step response and some maneuvers computed from the washout filter were used to evaluate the performance of the controllers.

Light emission and current rectification in a molecular device: Experiment and theory

We have investigated optical and transport properties of the molecular structure 2,3,4,5-tetraphenyl-1-phenylethynyl-cyclopenta-2,4-dienol experimentally and theoretically. The optical spectrum was calculated using Hartree-Fock-intermediate neglect of differential overlap-configuration interaction model. The experimental photoluminescence spectrum showed a peak around 470nm which was very well described by the modeling. Electronic transport measurements showed a diode-like effect with a strong current rectification. A phenomenological microscopic model based on non-equilibrium Green's function technique was proposed and a very good description electronic transport was obtained. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4767457]

Mathematical modeling and analysis of the particle interactions in the direct filtration using the colloidal theory

This work used the colloidal theory to describe forces and energy interactions of colloidal complexes in the water and those formed during filtration run in direct filtration. Many interactions of particle energy profiles between colloidal surfaces for three geometries are presented here in: spherical, plate and cylindrical; and four surface interactions arrangements: two cylinders, two spheres, two plates and a sphere and a plate. Two different situations were analyzed, before and after electrostatic destabilization by action of the alum sulfate as coagulant in water studies samples prepared with kaolin. In the case were used mathematical modeling by extended DLVO theory (from the names: Derjarguin-Landau-Verwey-Overbeek) or XDLVO, which include traditional approach of the electric double layer (EDL), surfaces attraction forces or London-van der Waals (LvdW), esteric forces and hydrophobic forces, additionally considering another forces in colloidal system, like molecular repulsion or Born Repulsion and Acid-Base (AB) chemical function forces from Lewis.

Ethanol and Water Adsorption on Close-Packed 3d, 4d, and 5d Transition-Metal Surfaces: A Density Functional Theory Investigation with van der Waals Correction

Nowadays, there is a great interest in the economic success of direct ethanol fuel cells; however, our atomistic understanding of the designing of stable and low-cost catalysts for the steam reforming of ethanol is still far from satisfactory, in particular due to the large number of undesirable intermediates. In this study, we will report a first-principles investigation of the adsorption properties of ethanol and water at low coverage on close-packed transition-metal (TM) surfaces, namely, Fe(110), Co(0001), Ni(111), Cu(111), Ru(0001), Rh(111), Pd(111), Ag(111), Os(0001), Ir(111), Pt(111), and Au(111), employing density functional theory (DFT) calculations. We employed the generalized gradient approximation with the formulation proposed by Perdew, Burke, and Erzenholf (PBE) to the exchange correlation functional and the empirical correction proposed by S. Grimme (DFT+D3) for the van der Waals correction. We found that both adsorbates binds preferentially near or on the on top sites of the TM surfaces through the 0 atoms. The PBE adsorption energies of ethanol and water decreases almost linearly with the increased occupation of the 4d and 5d d-band, while there is a deviation for the 3d systems. The van der Waals correction affects the linear behavior and increases the adsorption energy for both adsorbates, which is expected as the van der Waals energy due to the correlation effects is strongly underestimated by DFT-PBE for weak interacting systems. The geometric parameters for water/TM are not affected by the van der Waals correction, i.e., both DFT and DFT+D3 yield an almost parallel orientation for water on the TM surfaces; however, DFT+D3 changes drastically the ethanol orientation. For example, DFT yields an almost perpendicular orientation of the C-C bond to the TM surface, while the C-C bond is almost parallel to the surface using DFT +D3 for all systems, except for ethanol/Fe(110). Thus, the van der Waals correction decreases the distance of the C atoms to the TM surfaces, which might contribute to break the C-C bond. The work function decreases upon the adsorption of ethanol and water, and both follow the same trends, however, with different magnitude (larger for ethanol/TM) due to the weak binding of water to the surface. The electron density increases mainly in the region between the topmost layer and the adsorbates, which explains the reduction of the substrate work function.

Relationship between global structural parameters and Enzyme Commission hierarchy: Implications for function prediction

In protein databases there is a substantial number of proteins structurally determined but without function annotation. Understanding the relationship between function and structure can be useful to predict function on a large scale. We have analyzed the similarities in global physicochemical parameters for a set of enzymes which were classified according to the four Enzyme Commission (EC) hierarchical levels. Using relevance theory we introduced a distance between proteins in the space of physicochemical characteristics. This was done by minimizing a cost function of the metric tensor built to reflect the EC classification system. Using an unsupervised clustering method on a set of 1025 enzymes, we obtained no relevant clustering formation compatible with EC classification. The distance distributions between enzymes from the same EC group and from different EC groups were compared by histograms. Such analysis was also performed using sequence alignment similarity as a distance. Our results suggest that global structure parameters are not sufficient to segregate enzymes according to EC hierarchy. This indicates that features essential for function are rather local than global. Consequently, methods for predicting function based on global attributes should not obtain high accuracy in main EC classes prediction without relying on similarities between enzymes from training and validation datasets. Furthermore, these results are consistent with a substantial number of studies suggesting that function evolves fundamentally by recruitment, i.e., a same protein motif or fold can be used to perform different enzymatic functions and a few specific amino acids (AAs) are actually responsible for enzyme activity. These essential amino acids should belong to active sites and an effective method for predicting function should be able to recognize them. (C) 2012 Elsevier Ltd. All rights reserved.

Multibrane solutions in cubic superstring field theory

Using the elements of the so-called KBc gamma subalgebra, we study a class of analytic solutions depending on a single function F(K) in the modified cubic superstring field theory. We compute the energy associated to these solutions and show that the result can be expressed in terms of a contour integral. For a particular choice of the function F(K), we show that the energy is given by integer multiples of a single D-brane tension.

Evolution of form and function: morphophysiological relationships and locomotor performance in tropidurine lizards

Locomotor capacity is often considered an excellent measure of whole animal performance because it requires the integrated functioning of many morphological, physiological (and biochemical) traits. However, because studies tend to focus on either structural or functional suits of traits, we know little on whether and how morphological and physiological traits coevolve to produce adequate locomotor capacities. Hence, we investigate the evolutionary relationships between morphological and physiological parameters related to exercise physiology, using tropidurine lizards as a model. We employ a phylogenetic principal component analysis (PCA) to identify variable clusters (factors) related to morphology, energetic metabolism and muscle metabolism, and then analyze the relationships between these clusters and measures of locomotor performance, using two models (star and hierarchical phylogenies). Our data indicate that sprint performance is enhanced by simultaneous evolutionary tendencies affecting relative limb and tail size and physiological traits. Specifically, the high absolute sprint speeds exhibited by tropidurines from the sand dunes are explained by longer limbs, feet and tails and an increased proportion of glycolytic fibers in the leg muscle, contrasting with their lower capacity for overall oxidative metabolism [principal component (PC1)]. However, when sprint speeds are corrected for body size, performance correlates with a cluster (PC3) composed by moderate loads for activity metabolic rate and body size. The simultaneous measurement of morphological and physiological parameters is a powerful tool for exploring patterns of coadaptation and proposing morphophysiological associations that are not directly predictable from theory. This approach may trigger novel directions for investigating the evolution of form and function, particularly in the context of organismal performance.

Magnetic hyperthermia investigation of cobalt ferrite nanoparticles: Comparison between experiment, linear response theory, and dynamic hysteresis simulations

Considerable effort has been made in recent years to optimize materials properties for magnetic hyperthermia applications. However, due to the complexity of the problem, several aspects pertaining to the combined influence of the different parameters involved still remain unclear. In this paper, we discuss in detail the role of the magnetic anisotropy on the specific absorption rate of cobalt-ferrite nanoparticles with diameters ranging from 3 to 14 nm. The structural characterization was carried out using x-ray diffraction and Rietveld analysis and all relevant magnetic parameters were extracted from vibrating sample magnetometry. Hyperthermia investigations were performed at 500 kHz with a sinusoidal magnetic field amplitude of up to 68 Oe. The specific absorption rate was investigated as a function of the coercive field, saturation magnetization, particle size, and magnetic anisotropy. The experimental results were also compared with theoretical predictions from the linear response theory and dynamic hysteresis simulations, where exceptional agreement was found in both cases. Our results show that the specific absorption rate has a narrow and pronounced maxima for intermediate anisotropy values. This not only highlights the importance of this parameter but also shows that in order to obtain optimum efficiency in hyperthermia applications, it is necessary to carefully tailor the materials properties during the synthesis process. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4729271]

Platinum-Based Nanoalloys PtnTM55-n (TM=Co, Rh, Au): A Density Functional Theory Investigation

Structural and electronic properties of the PtnTM55-n (TM = Co, Rh, Au) nanoalloys are investigated using density functional theory within the generalized gradient approximation and employing the all-electron projected augmented wave method. For TM = Co and Rh, the excess energy, which measures the relative energy stability of the nanoalloys, is negative for all Pt compositions. We found that the excess energy has similar values for a wide range of Pt compositions, i.e., n = 20-42 and n = 28-42 for Co and Rh, respectively, with the core shell icosahedron-like configuration (n = 42) being slightly more stable for both Co and Rh systems because of the larger release of the strain energy due to the smaller atomic size of the Co and Rh atoms. For TM = Au, the excess energy is positive for all compositions, except for n = 13, which is energetically favorable due to the formation of the core-shell structure (Pt in the core and Au atoms at the surface). Thus, our calculations confirm that the formation of core-shell structures plays an important role to increase the stability of nanoalloys. The center of gravity of the occupied d-states changes almost linearly as a function of the Pt composition, and hence, based on the d-band model, the magnitude of the adsorption energy of an adsorbate can be tuned by changing the Pt composition. The magnetic moments of PtnCo55-n decrease almost linearly as a function of the Pt composition; however, the same does not hold for PtRh and PtAu. We found an enhancement of the magnetic moments of PtRh by a few times by increasing Pt composition, which we explain by the compression effects induced by the large size of the Pt atoms compared with the Rh atoms.

Application of H∞ theory to a 6 DOF flight simulator motion base

The purpose of this study is to apply inverse dynamics control for a six degree of freedom flight simulator motion system. Imperfect compensation of the inverse dynamic control is intentionally introduced in order to simplify the implementation of this approach. The control strategy is applied in the outer loop of the inverse dynamic control to counteract the effects of imperfect compensation. The control strategy is designed using H∞ theory. Forward and inverse kinematics and full dynamic model of a six degrees of freedom motion base driven by electromechanical actuators are briefly presented. Describing function, acceleration step response and some maneuvers computed from the washout filter were used to evaluate the performance of the controllers.

Computational analyses on the structure-function relation in ion channels

Ion channels are protein molecules, embedded in the lipid bilayer of the cell membranes. They act as powerful sensing elements switching chemicalphysical stimuli into ion-fluxes. At a glance, ion channels are water-filled pores, which can open and close in response to different stimuli (gating), and one once open select the permeating ion species (selectivity). They play a crucial role in several physiological functions, like nerve transmission, muscular contraction, and secretion. Besides, ion channels can be used in technological applications for different purpose (sensing of organic molecules, DNA sequencing). As a result, there is remarkable interest in understanding the molecular determinants of the channel functioning. Nowadays, both the functional and the structural characteristics of ion channels can be experimentally solved. The purpose of this thesis was to investigate the structure-function relation in ion channels, by computational techniques. Most of the analyses focused on the mechanisms of ion conduction, and the numerical methodologies to compute the channel conductance. The standard techniques for atomistic simulation of complex molecular systems (Molecular Dynamics) cannot be routinely used to calculate ion fluxes in membrane channels, because of the high computational resources needed. The main step forward of the PhD research activity was the development of a computational algorithm for the calculation of ion fluxes in protein channels. The algorithm - based on the electrodiffusion theory - is computational inexpensive, and was used for an extensive analysis on the molecular determinants of the channel conductance. The first record of ion-fluxes through a single protein channel dates back to 1976, and since then measuring the single channel conductance has become a standard experimental procedure. Chapter 1 introduces ion channels, and the experimental techniques used to measure the channel currents. The abundance of functional data (channel currents) does not match with an equal abundance of structural data. The bacterial potassium channel KcsA was the first selective ion channels to be experimentally solved (1998), and after KcsA the structures of four different potassium channels were revealed. These experimental data inspired a new era in ion channel modeling. Once the atomic structures of channels are known, it is possible to define mathematical models based on physical descriptions of the molecular systems. These physically based models can provide an atomic description of ion channel functioning, and predict the effect of structural changes. Chapter 2 introduces the computation methods used throughout the thesis to model ion channels functioning at the atomic level. In Chapter 3 and Chapter 4 the ion conduction through potassium channels is analyzed, by an approach based on the Poisson-Nernst-Planck electrodiffusion theory. In the electrodiffusion theory ion conduction is modeled by the drift-diffusion equations, thus describing the ion distributions by continuum functions. The numerical solver of the Poisson- Nernst-Planck equations was tested in the KcsA potassium channel (Chapter 3), and then used to analyze how the atomic structure of the intracellular vestibule of potassium channels affects the conductance (Chapter 4). As a major result, a correlation between the channel conductance and the potassium concentration in the intracellular vestibule emerged. The atomic structure of the channel modulates the potassium concentration in the vestibule, thus its conductance. This mechanism explains the phenotype of the BK potassium channels, a sub-family of potassium channels with high single channel conductance. The functional role of the intracellular vestibule is also the subject of Chapter 5, where the affinity of the potassium channels hEag1 (involved in tumour-cell proliferation) and hErg (important in the cardiac cycle) for several pharmaceutical drugs was compared. Both experimental measurements and molecular modeling were used in order to identify differences in the blocking mechanism of the two channels, which could be exploited in the synthesis of selective blockers. The experimental data pointed out the different role of residue mutations in the blockage of hEag1 and hErg, and the molecular modeling provided a possible explanation based on different binding sites in the intracellular vestibule. Modeling ion channels at the molecular levels relates the functioning of a channel to its atomic structure (Chapters 3-5), and can also be useful to predict the structure of ion channels (Chapter 6-7). In Chapter 6 the structure of the KcsA potassium channel depleted from potassium ions is analyzed by molecular dynamics simulations. Recently, a surprisingly high osmotic permeability of the KcsA channel was experimentally measured. All the available crystallographic structure of KcsA refers to a channel occupied by potassium ions. To conduct water molecules potassium ions must be expelled from KcsA. The structure of the potassium-depleted KcsA channel and the mechanism of water permeation are still unknown, and have been investigated by numerical simulations. Molecular dynamics of KcsA identified a possible atomic structure of the potassium-depleted KcsA channel, and a mechanism for water permeation. The depletion from potassium ions is an extreme situation for potassium channels, unlikely in physiological conditions. However, the simulation of such an extreme condition could help to identify the structural conformations, so the functional states, accessible to potassium ion channels. The last chapter of the thesis deals with the atomic structure of the !- Hemolysin channel. !-Hemolysin is the major determinant of the Staphylococcus Aureus toxicity, and is also the prototype channel for a possible usage in technological applications. The atomic structure of !- Hemolysin was revealed by X-Ray crystallography, but several experimental evidences suggest the presence of an alternative atomic structure. This alternative structure was predicted, combining experimental measurements of single channel currents and numerical simulations. This thesis is organized in two parts, in the first part an overview on ion channels and on the numerical methods adopted throughout the thesis is provided, while the second part describes the research projects tackled in the course of the PhD programme. The aim of the research activity was to relate the functional characteristics of ion channels to their atomic structure. In presenting the different research projects, the role of numerical simulations to analyze the structure-function relation in ion channels is highlighted.

The massless two-loop two-point function and zeta functions in counterterms of Feynman diagrams

The main part of this thesis describes a method of calculating the massless two-loop two-point function which allows expanding the integral up to an arbitrary order in the dimensional regularization parameter epsilon by rewriting it as a double Mellin-Barnes integral. Closing the contour and collecting the residues then transforms this integral into a form that enables us to utilize S. Weinzierl's computer library nestedsums. We could show that multiple zeta values and rational numbers are sufficient for expanding the massless two-loop two-point function to all orders in epsilon. We then use the Hopf algebra of Feynman diagrams and its antipode, to investigate the appearance of Riemann's zeta function in counterterms of Feynman diagrams in massless Yukawa theory and massless QED. The class of Feynman diagrams we consider consists of graphs built from primitive one-loop diagrams and the non-planar vertex correction, where the vertex corrections only depend on one external momentum. We showed the absence of powers of pi in the counterterms of the non-planar vertex correction and diagrams built by shuffling it with the one-loop vertex correction. We also found the invariance of some coefficients of zeta functions under a change of momentum flow through these vertex corrections.

Pseudodifferential analysis in Psi*-algebras on transmission spaces, infinite solving ideal chains and K-theory for conformally compact spaces

The present thesis is a contribution to the theory of algebras of pseudodifferential operators on singular settings. In particular, we focus on the $b$-calculus and the calculus on conformally compact spaces in the sense of Mazzeo and Melrose in connection with the notion of spectral invariant transmission operator algebras. We summarize results given by Gramsch et. al. on the construction of $Psi_0$-and $Psi*$-algebras and the corresponding scales of generalized Sobolev spaces using commutators of certain closed operators and derivations. In the case of a manifold with corners $Z$ we construct a $Psi*$-completion $A_b(Z,{}^bOmega^{1/2})$ of the algebra of zero order $b$-pseudodifferential operators $Psi_{b,cl}(Z, {}^bOmega^{1/2})$ in the corresponding $C*$-closure $B(Z,{}^bOmega^{12})hookrightarrow L(L^2(Z,{}^bOmega^{1/2}))$. The construction will also provide that localised to the (smooth) interior of Z the operators in the $A_b(Z, {}^bOmega^{1/2})$ can be represented as ordinary pseudodifferential operators. In connection with the notion of solvable $C*$-algebras - introduced by Dynin - we calculate the length of the $C*$-closure of $Psi_{b,cl}^0(F,{}^bOmega^{1/2},R^{E(F)})$ in $B(F,{}^bOmega^{1/2}),R^{E(F)})$ by localizing $B(Z, {}^bOmega^{1/2})$ along the boundary face $F$ using the (extended) indical familiy $I^B_{FZ}$. Moreover, we discuss how one can localise a certain solving ideal chain of $B(Z, {}^bOmega^{1/2})$ in neighbourhoods $U_p$ of arbitrary points $pin Z$. This localisation process will recover the singular structure of $U_p$; further, the induced length function $l_p$ is shown to be upper semi-continuous. We give construction methods for $Psi*$- and $C*$-algebras admitting only infinite long solving ideal chains. These algebras will first be realized as unconnected direct sums of (solvable) $C*$-algebras and then refined such that the resulting algebras have arcwise connected spaces of one dimensional representations. In addition, we recall the notion of transmission algebras on manifolds with corners $(Z_i)_{iin N}$ following an idea of Ali Mehmeti, Gramsch et. al. Thereby, we connect the underlying $C^infty$-function spaces using point evaluations in the smooth parts of the $Z_i$ and use generalized Laplacians to generate an appropriate scale of Sobolev spaces. Moreover, it is possible to associate generalized (solving) ideal chains to these algebras, such that to every $ninN$ there exists an ideal chain of length $n$ within the algebra. Finally, we discuss the $K$-theory for algebras of pseudodifferential operators on conformally compact manifolds $X$ and give an index theorem for these operators. In addition, we prove that the Dirac-operator associated to the metric of a conformally compact manifold $X$ is not a Fredholm operator.

Low Correlated Sequences & Architectures and Algorithms for Analog-to-Information Converters: Theory, Design, Implementation and Applications.

Most electronic systems can be described in a very simplified way as an assemblage of analog and digital components put all together in order to perform a certain function. Nowadays, there is an increasing tendency to reduce the analog components, and to replace them by operations performed in the digital domain. This tendency has led to the emergence of new electronic systems that are more flexible, cheaper and robust. However, no matter the amount of digital process implemented, there will be always an analog part to be sorted out and thus, the step of converting digital signals into analog signals and vice versa cannot be avoided. This conversion can be more or less complex depending on the characteristics of the signals. Thus, even if it is desirable to replace functions carried out by analog components by digital processes, it is equally important to do so in a way that simplifies the conversion from digital to analog signals and vice versa. In the present thesis, we have study strategies based on increasing the amount of processing in the digital domain in such a way that the implementation of analog hardware stages can be simplified. To this aim, we have proposed the use of very low quantized signals, i.e. 1-bit, for the acquisition and for the generation of particular classes of signals.