Integrability vs supersymmetry: Poisson structures of the pohlmeyer reduction

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Generalizations of Poisson Structures Related to Rational Gaudin Model

International audience

Rigid body trajectories in different 6D spaces

The objective of this paper is to show that the group SE(3) with an imposed Lie-Poisson structure can be used to determine the trajectory in a spatial frame of a rigid body in Euclidean space. Identical results for the trajectory are obtained in spherical and hyperbolic space by scaling the linear displacements appropriately since the influence of the moments of inertia on the trajectories tends to zero as the scaling factor increases. The semidirect product of the linear and rotational motions gives the trajectory from a body frame perspective. It is shown that this cannot be used to determine the trajectory in the spatial frame. The body frame trajectory is thus independent of the velocity coupling. In addition, it is shown that the analysis can be greatly simplified by aligning the axes of the spatial frame with the axis of symmetry which is unchanging for a natural system with no forces and rotation about an axis of symmetry.

Star products made (somewhat) easier

We develop an approach to the deformation quantization on the real plane with an arbitrary Poisson structure which is based on Weyl symmetrically ordered operator products. By using a polydifferential representation for the deformed coordinates, xj we are able to formulate a simple and effective iterative procedure which allowed us to calculate the fourth-order star product (and may be extended to the fifth order at the expense of tedious but otherwise straightforward calculations). Modulo some cohomology issues which we do not consider here, the method gives an explicit and physics-friendly description of the star products.

Supersymmetry flows, semi-symmetric space sine-Gordon models and the Pohlmeyer reduction

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Primitive Ideals and Symplectic Leaves of Quantum Matrices

It is proved that there exists a bijection between the primitive ideals of the algebra of regular functions on quantum m × n-matrices and the symplectic leaves of associated Poisson structure.

Studies on the Cell Wall Structure and on the Mechanical Properties of Norway Spruce

The structure and the mechanical properties of wood of Norway spruce (Picea abies [L.] Karst.) were studied using small samples from Finland and Sweden. X-ray diffraction (XRD) was used to determine the orientation of cellulose microfibrils (microfibril angle, MFA), the dimensions of cellulose crystallites and the average shape of the cell cross-section. X-ray attenuation and x-ray fluorescence measurements were used to study the chemical composition and the trace element content. Tensile testing with in situ XRD was used to characterise the mechanical properties of wood and the deformation of crystalline cellulose within the wood cell walls. Cellulose crystallites were found to be 192 284 Å long and 28.9 33.4 Å wide in chemically untreated wood and they were longer and wider in mature wood than in juvenile wood. The MFA distribution of individual Norway spruce tracheids and larger samples was asymmetric. In individual cell walls, the mean MFA was 19 30 degrees, while the mode of the MFA distribution was 7 21 degrees. Both the mean MFA and the mode of the MFA distribution decreased as a function of the annual ring. Tangential cell walls exhibited smaller mean MFA and mode of the MFA distribution than radial cell walls. Maceration of wood material caused narrowing of the MFA distribution and removed contributions observed at around 90 degrees. In wood of both untreated and fertilised trees, the average shape of the cell cross-section changed from circular via ambiguous to rectangular as the cambial age increased. The average shape of the cell cross-section and the MFA distribution did not change as a result of fertilisation. The mass absorption coefficient for x-rays was higher in wood of fertilised trees than in that of untreated trees and wood of fertilised trees contained more of the elements S, Cl, and K, but a smaller amount of Mn. Cellulose crystallites were longer in wood of fertilised trees than in that of untreated trees. Kraft cooking caused widening and shortening of the cellulose crystallites. Tensile tests parallel to the cells showed that if the mean MFA is initially around 10 degrees or smaller, no systematic changes occur in the MFA distribution due to strain. The role of mean MFA in defining the tensile strength or the modulus of elasticity of wood was not as dominant as that reported earlier. Crystalline cellulose elongated much less than the entire samples. The Poisson ratio νca of crystalline cellulose in Norway spruce wood was shown to be largely dependent on the surroundings of crystalline cellulose in the cell wall, varying between -1.2 and 0.8. The Poisson ratio was negative in kraft cooked wood and positive in chemically untreated wood. In chemically untreated wood, νca was larger in mature wood and in latewood compared to juvenile wood and earlywood.

A mathematical programming approach to optimal Markovian switching of Poisson arrival streams to queueing systems

Motivated by certain situations in manufacturing systems and communication networks, we look into the problem of maximizing the profit in a queueing system with linear reward and cost structure and having a choice of selecting the streams of Poisson arrivals according to an independent Markov chain. We view the system as a MMPP/GI/1 queue and seek to maximize the profits by optimally choosing the stationary probabilities of the modulating Markov chain. We consider two formulations of the optimization problem. The first one (which we call the PUT problem) seeks to maximize the profit per unit time whereas the second one considers the maximization of the profit per accepted customer (the PAC problem). In each of these formulations, we explore three separate problems. In the first one, the constraints come from bounding the utilization of an infinite capacity server; in the second one the constraints arise from bounding the mean queue length of the same queue; and in the third one the finite capacity of the buffer reflect as a set of constraints. In the problems bounding the utilization factor of the queue, the solutions are given by essentially linear programs, while the problems with mean queue length constraints are linear programs if the service is exponentially distributed. The problems modeling the finite capacity queue are non-convex programs for which global maxima can be found. There is a rich relationship between the solutions of the PUT and PAC problems. In particular, the PUT solutions always make the server work at a utilization factor that is no less than that of the PAC solutions.

EFFECT OF CORE-SHELL STRUCTURE OF HYDROGEL BEADS ON THE THRESHOLD CONCENTRATION OF WATER FOR SWELLING AND ITS PH SENSITIVITY

In this paper we investigate the effect of core-shell structure of Sodium Alginate based hydrogel beads and their size on certain activation threshold concentration of water for applications in swelling and pH sensing. This type of hydrogel experiences diffusive pressure due to transport of certain free charges across its interface with a solvent or electrolyte. This process is essentially a dynamic equilibrium of the electric force field, stress in the polymeric network with cage like structure and molecular diffusion including phase transformation due to pressure imbalance between the hydrogel and its surroundings. The effect of pH of the solvant on the swelling rate of these beads has been studied experimentally. A mathematical model of the swelling process has been developed by considering Nernst-Planck equation representing the migration of mobile ions and Er ions, Poisson equation representing the equilibrium of the electric field and mechanical field equation representing swelling of the gel. An attempt has been made to predict the experimentally observed phenomena using these numerical simulations. It is observed experimentally that certain minimum concentration called activation threshold concentration of the water molecules must be present in the hydrogel in order to activate the swelling process. For the required activation threshold concentration of water in the beads, the pH induced change in the rate of swelling is also investigated. This effect is analyzed for various different core-shell structures of the beads.

In-plane elastic responses of circular cell honeycombs and bundled circular tubes in a diamond array structure

Assemblages of circular tubes and circular honeycombs in close packed arrangement are presently both competing and complementing regular honeycomb structures (HCS). The intrinsic isotropy of bundled tubes/rings in hexagonal arrays restricts their use to applications with isotopic need. With the aim of extending the utility of tubes/rings assemblages to anisotropic needs, this paper explores the prospects of bundled tubes and circular honeycombs in a general diamond array structure (DAS) to cater these needs. To this end, effective transverse Young's moduli and Poisson's ratio for thick/thin DAS are obtained theoretically. Analysis frameworks including thin ring theory (TRT), curved beam theory (CBT) and elasticity formulations are tested and corroborated by FEA employing contact elements. Results indicate that TRT and CBT are reasonable for thin tubes and honeycombs. Nevertheless, TRT yields compact formulae to study the anisotropy ratio, moduli spectrum and sensitivity of the assemblage as a function of thicknesses and array structure. These formulae supplement designers as a guide to tailor the structures. On the other hand, elasticity formulation can estimate over a larger range including very thick tubes/rings. In addition, this formulation offers to estimate refined transverse strengths of assemblages. (C) 2015 Elsevier Ltd. All rights reserved.

Hierarchy of structure functions for passive scalars advected by turbulent flows

A hierarchical model is proposed for the joint moments of the passive scalar dissipation and the velocity dissipation in fluid turbulence. This model predicts that the joint probability density function (PDF) of the dissipations is a bivariate log-Poisson. An analytical calculation of the scaling exponents of structure functions of the passive scalar is carried out for this hierarchical model, showing a good agreement with the results of direct numerical simulations and experiments.

Thermodynamical versus log-Poisson distribution in turbulence

The thermodynamical model of intermittency in fully developed turbulence due to Castaing (B. Castaing, J. Phys. II France 6 (1996) 105) is investigated and compared with the log-Poisson model (Z-S, She, E. Leveque, Phys. Rev. Lett. 72 (1994) 336). It is shown that the thermodynamical model obeys general scaling laws and corresponds to the degenerate class of scale-invariant statistics. We also find that its structure function shapes have physical behaviors similar to the log-Poisson's one. The only difference between them lies in the convergence of the log-Poisson's structure functions and divergence of the thermodynamical one. As far as the comparison with experiments on intermittency is concerned, they are indifferent.

Analysis of temporal structure in spike trains of visual cortical area MT

The temporal structure of neuronal spike trains in the visual cortex can provide detailed information about the stimulus and about the neuronal implementation of visual processing. Spike trains recorded from the macaque motion area MT in previous studies (Newsome et al., 1989a; Britten et al., 1992; Zohary et al., 1994) are analyzed here in the context of the dynamic random dot stimulus which was used to evoke them. If the stimulus is incoherent, the spike trains can be highly modulated and precisely locked in time to the stimulus. In contrast, the coherent motion stimulus creates little or no temporal modulation and allows us to study patterns in the spike train that may be intrinsic to the cortical circuitry in area MT. Long gaps in the spike train evoked by the preferred direction motion stimulus are found, and they appear to be symmetrical to bursts in the response to the anti-preferred direction of motion. A novel cross-correlation technique is used to establish that the gaps are correlated between pairs of neurons. Temporal modulation is also found in psychophysical experiments using a modified stimulus. A model is made that can account for the temporal modulation in terms of the computational theory of biological image motion processing. A frequency domain analysis of the stimulus reveals that it contains a repeated power spectrum that may account for psychophysical and electrophysiological observations.

Some neurons tend to fire bursts of action potentials while others avoid burst firing. Using numerical and analytical models of spike trains as Poisson processes with the addition of refractory periods and bursting, we are able to account for peaks in the power spectrum near 40 Hz without assuming the existence of an underlying oscillatory signal. A preliminary examination of the local field potential reveals that stimulus-locked oscillation appears briefly at the beginning of the trial.

Effects of self energy of the ions on the double layer structure and properties at the dielectric interface

Although numerous theoretical efforts have been put forth, a systematic, unified and predictive theoretical framework that is able to capture all the essential physics of the interfacial behaviors of ions, such as the Hofmeister series effect, Jones-Ray effect and the salt effect on the bubble coalescence remain an outstanding challenge. The most common approach to treating electrostatic interactions in the presence of salt ions is the Poisson-Boltzmann (PB) theory. However, there are many systems for which the PB theory fails to offer even a qualitative explanation of the behavior, especially for ions distributed in the vicinity of an interface with dielectric contrast between the two media (like the water-vapor/oil interface). A key factor missing in the PB theory is the self energy of the ion.

In this thesis, we develop a self-consistent theory that treats the electrostatic self energy (including both the short-range Born solvation energy and the long-range image charge interactions), the nonelectrostatic contribution of the self energy, the ion-ion correlation and the screening effect systematically in a single framework. By assuming a finite charge spread of the ion instead of using the point-charge model, the self energy obtained by our theory is free of the divergence problems and gives a continuous self energy across the interface. This continuous feature allows ions on the water side and the vapor/oil side of the interface to be treated in a unified framework. The theory involves a minimum set of parameters of the ion, such as the valency, radius, polarizability of the ions, and the dielectric constants of the medium, that are both intrinsic and readily available. The general theory is first applied to study the thermodynamic property of the bulk electrolyte solution, which shows good agreement with the experiment result for predicting the activity coefficient and osmotic coefficient.

Next, we address the effect of local Born solvation energy on the bulk thermodynamics and interfacial properties of electrolyte solution mixtures. We show that difference in the solvation energy between the cations and anions naturally gives rise to local charge separation near the interface, and a finite Galvani potential between two coexisting solutions. The miscibility of the mixture can either increases or decreases depending on the competition between the solvation energy and translation entropy of the ions. The interfacial tension shows a non-monotonic dependence on the salt concentration: it increases linearly with the salt concentration at higher concentrations, and decreases approximately as the square root of the salt concentration for dilute solutions, which is in agreement with the Jones-Ray effect observed in experiment.

Next, we investigate the image effects on the double layer structure and interfacial properties near a single charged plate. We show that the image charge repulsion creates a depletion boundary layer that cannot be captured by a regular perturbation approach. The correct weak-coupling theory must include the self-energy of the ion due to the image charge interaction. The image force qualitatively alters the double layer structure and properties, and gives rise to many non-PB effects, such as nonmonotonic dependence of the surface energy on concentration and charge inversion. The image charge effect is then studied for electrolyte solutions between two plates. For two neutral plates, we show that depletion of the salt ions by the image charge repulsion results in short-range attractive and long-range repulsive forces. If cations and anions are of different valency, the asymmetric depletion leads to the formation of an induced electrical double layer. For two charged plates, the competition between the surface charge and the image charge effect can give rise to like- charge attraction.

Then, we study the inhomogeneous screening effect near the dielectric interface due to the anisotropic and nonuniform ion distribution. We show that the double layer structure and interfacial properties is drastically affected by the inhomogeneous screening if the bulk Debye screening length is comparable or smaller than the Bjerrum length. The width of the depletion layer is characterized by the Bjerrum length, independent of the salt concentration. We predict that the negative adsorption of ions at the interface increases linearly with the salt concentration, which cannot be captured by either the bulk screening approximation or the WKB approximation. For asymmetric salt, the inhomogeneous screening enhances the charge separation in the induced double layer and significantly increases the value of the surface potential.

Finally, to account for the ion specificity, we study the self energy of a single ion across the dielectric interface. The ion is considered to be polarizable: its charge distribution can be self-adjusted to the local dielectric environment to minimize the self energy. Using intrinsic parameters of the ions, such as the valency, radius, and polarizability, we predict the specific ion effect on the interfacial affinity of halogen anions at the water/air interface, and the strong adsorption of hydrophobic ions at the water/oil interface, in agreement with experiments and atomistic simulations.

The theory developed in this work represents the most systematic theoretical technique for weak-coupling electrolytes. We expect the theory to be more useful for studying a wide range of structural and dynamic properties in physicochemical, colloidal, soft-matter and biophysical systems.

The influence of 1 nm AlN interlayer on properties of the Al0.3Ga0.7N/AlN/GaN HEMT structure

The sheet carrier concentrations, conduction band profiles and amount of free carriers in the barriers have been determined by solving coupled Schrodinger and Poisson equation self-consistently for coherently grown Al0.3Ga0.7N/GaN and Al0.3Ga0.7N/AlN/GaN structures on thick GaN. The Al0.3Ga0.7N/GaN heterojunction structures with and without 1 nm AlN interlayer have been grown by MOCVD on sapphire substrate, the physical properties for these two structures have been investigated by various instruments such as Hall measurement and X-ray diffraction. By comparison of the theoretical and experimental results, we demonstrate that the sheet carrier concentration and the electrons mobility would be improved by the introduction of an AlN interlayer for Al0.3Ga0.7N/GaN structure. Mechanisms for the increasing of the sheet carrier concentration and the electrons mobility will be discussed in this paper. (C) 2007 Elsevier Ltd. All rights reserved.