Non-equilibrium segmental dynamics driven by multiwall carbon nanotubes in PS/PVME blends

The present paper discusses the effect of multiwall carbon nanotubes (MWNTs) on the structural relaxation and the intermolecular cooperativity in dynamically asymmetric blends of PS/PVME (polystyrene/poly(vinyl methyl ether)). The temperature regime where chain connectivity effects dominate the thermodynamic concentration fluctuation (T/T-g > 0.75, T-g is the glass transition temperature of the blends) was studied using dielectric spectroscopy (DS). Interestingly, in the blends with MWNTs a bimodal distribution of relaxation was obtained in the loss modulus spectra. This plausibly is due to different environments experienced by the faster component (PVME) in the presence of MWNTs. The segmental dynamics of PVME was observed to be significantly slowed down in the presence of MWNTs and an Arrhenius-type behavior, weakly dependent on temperature, is observed at higher frequencies. This non-equilibrium dynamics of PVME is presumed to be originating from interphase regions near the surface of MWNTs. The length scale of the cooperative rearranging region (xi CRR) at T-g, assessed by calorimetric measurements, was observed to be higher in the case of blends with MWNTs. An enhanced molecular level miscibility driven by MWNTs in the blends corroborates with the larger xi CRR and comparatively more number of segments in CRR (in contrast to neat blends) around T-g. The configurational entropy and length scale of the cooperative volume was mapped as a function of temperature in the temperature regime, Tg < T < T-g + 60 K. The blends phase separated by spinodal decomposition which further led to an interconnected PVME network in PS. This further led to materials with very high electrical conductivity upon demixing.

Strings vs. spins on the null orbifold

We study the null orbifold singularity in 2+1 d flat space higher spin theory as well as string theory. Using the Chern-Simons formulation of 2+1 d Einstein gravity, we first observe that despite the singular nature of this geometry, the eigenvalues of its Chern-Simons holonomy are trivial. Next, we construct a resolution of the singularity in higher spin theory: a Kundt spacetime with vanishing scalar curvature invariants. We also point out that the UV divergences previously observed in the 2-to-2 tachyon tree level string amplitude on the null orbifold do not arise in the at alpha' -> infinity limit. We find all the divergences of the amplitude and demonstrate that the ones remaining in the tensionless limit are physical IR-type divergences. We conclude with a discussion on the meaning and limitations of higher spin (cosmological) singularity resolution and its potential connection to string theory.

Improving the Rigor and Consistency of the Thermodynamic Theory for Clathrate Hydrates through Incorporation of Movement of Water Molecules of Hydrate Lattice

Current applications of statistical thermodynamic theories for clathrate hydrates do not incorporate the translational and rotational movement of water molecules of the hydrate lattice,in a rigorous manner. Previous studies have shown that the movement of water molecules has a significant effect on the properties of clathrate hydrates. In this Article, a method is presented to incorporate the effect of water movement with as much rigor as possible. This method is then used to calculate the Langmuir constant of the guest species in a clathrate hydrate. Unlike previous studies on modeling of clathrate hydrate thermodynamics, the method presented in this paper does not regress either the intermolecular potentials or the properties of the empty hydrate from clathrate phase equilibria data. Also the properties of empty hydrate used in the theory do not depend on the nature and composition of the guest molecules. The predicted phase equilibria from the resulting theory are shown to be highly accurate and thermodynamically consistent by comparing them with the phase equilibria computed directly from molecular simulations.

Conformal perturbation theory and higher spin entanglement entropy on the torus

We study the free fermion theory in 1+1 dimensions deformed by chemical potentials for holomorphic, conserved currents at finite temperature and on a spatial circle. For a spin-three chemical potential mu, the deformation is related at high temperatures to a higher spin black hole in hs0] theory on AdS(3) spacetime. We calculate the order mu(2) corrections to the single interval Renyi and entanglement entropies on the torus using the bosonized formulation. A consistent result, satisfying all checks, emerges upon carefully accounting for both perturbative and winding mode contributions in the bosonized language. The order mu(2) corrections involve integrals that are finite but potentially sensitive to contact term singularities. We propose and apply a prescription for defining such integrals which matches the Hamiltonian picture and passes several non-trivial checks for both thermal corrections and the Renyi entropies at this order. The thermal corrections are given by a weight six quasi-modular form, whilst the Renyi entropies are controlled by quasi-elliptic functions of the interval length with modular weight six. We also point out the well known connection between the perturbative expansion of the partition function in powers of the spin-three chemical potential and the Gross-Taylor genus expansion of large-N Yang-Mills theory on the torus. We note the absence of winding mode contributions in this connection, which suggests qualitatively different entanglement entropies for the two systems.

Altruism in the (Social) Network

This paper explores the role of social integration on altruistic behavior. To this aim, we develop a two-stage experimental protocol based on the classic Dictator Game. In the first stage, we ask a group of 77 undergraduate students in Economics to elicit their social network; in the second stage, each of them has to unilaterally decide over the division of a fixed amount of money to be shared with another anonymous member in the group. Our experimental design allows to control for other variables known to be relevant for altruistic behavior: framing and friendship/acquaintance relations. Consistently with previous research, we find that subjects favor their friends and that framing enhances altruistic behavior. Once we control for these effects, social integration (measured by betweenness, a standard centrality measure in network theory) has a positive effect on giving: the larger social isolation within the group, the more likely it is the emergence of selfish behavior. These results suggest that information on the network structure in which subjects are embedded is crucial to account for their behavior.

Investment in the training of technologists for commercial aquaculture

The protein shortage in Nigeria is noted and the role of aquaculture (=fish farming) as a complement in increasing the dwindling food supply is registered. In addition, the manpower shortage especially in the technology cadre is noted and attributed to the lack of co-ordination and standard curricula especially in aquaculture. An inventory of tasks performed in the aquaculture industry was taken and these were classified and validated, then their final priority level was used to assess which ones were critical, important or desirable and which ones would result in disaster or not with inadequate mastery. Based on the above, recommendations are made that all critical and important tasks be included in the teaching curriculum for aquaculture in both theory and practicals: while it is advocated that all tasks listed be undertaken in fish farm operations. This will raise the competence of technologists to run the commercial aquaculture projects

Experimental Study Of Vortex-Induced Vibrations Of A Cylinder Near A Rigid Plane Boundary In Steady Flow

In this study, the vortex-induced vibrations of a cylinder near a rigid plane boundary in a steady flow are studied experimentally. The phenomenon of vortex-induced vibrations of the cylinder near the rigid plane boundary is reproduced in the flume. The vortex shedding frequency and mode are also measured by the methods of hot film velocimeter and hydrogen bubbles. A parametric study is carried out to investigate the influences of reduced velocity, gap-to-diameter ratio, stability parameter and mass ratio on the amplitude and frequency responses of the cylinder. Experimental results indicate: (1) the Strouhal number (St) is around 0.2 for the stationary cylinder near a plane boundary in the sub-critical flow regime; (2) with increasing gap-to-diameter ratio (e (0)/D), the amplitude ratio (A/D) gets larger but frequency ratio (f/f (n) ) has a slight variation for the case of larger values of e (0)/D (e (0)/D > 0.66 in this study); (3) there is a clear difference of amplitude and frequency responses of the cylinder between the larger gap-to-diameter ratios (e (0)/D > 0.66) and the smaller ones (e (0)/D < 0.3); (4) the vibration of the cylinder is easier to occur and the range of vibration in terms of V (r) number becomes more extensive with decrease of the stability parameter, but the frequency response is affected slightly by the stability parameter; (5) with decreasing mass ratio, the width of the lock-in ranges in terms of V (r) and the frequency ratio (f/f (n) ) become larger.

Topics in linear and nonlinear dispersive waves

The various singularities and instabilities which arise in the modulation theory of dispersive wavetrains are studied. Primary interest is in the theory of nonlinear waves, but a study of associated questions in linear theory provides background information and is of independent interest.

The full modulation theory is developed in general terms. In the first approximation for slow modulations, the modulation equations are solved. In both the linear and nonlinear theories, singularities and regions of multivalued modulations are predicted. Higher order effects are considered to evaluate this first order theory. An improved approximation is presented which gives the true behavior in the singular regions. For the linear case, the end result can be interpreted as the overlap of elementary wavetrains. In the nonlinear case, it is found that a sufficiently strong nonlinearity prevents this overlap. Transition zones with a predictable structure replace the singular regions.

For linear problems, exact solutions are found by Fourier integrals and other superposition techniques. These show the true behavior when breaking modulations are predicted.

A numerical study is made for the anharmonic lattice to assess the nonlinear theory. This confirms the theoretical predictions of nonlinear group velocities, group splitting, and wavetrain instability, as well as higher order effects in the singular regions.

The hydro-kinetic theory of liquid helium II

In Part I the kinetic theory of excitations in flowing liquid He II is developed to a higher order than that carried out previously, by Landau and Khalatnikov, in order to demonstrate the existence of non-equilibrium terms of a new nature in the hydrodynamic equations. It is then shown that these terms can lead to spontaneous destabilization in counter currents when the relative velocity of the normal and super fluids exceeds a critical value that depends on the temperature, but not on geometry. There are no adjustable parameters in the theory. The critical velocities are estimated to be in the 14-20 m/sec range for T ≤ 2.0° K, but tend to zero as T → T_λ. The possibility that these critical velocities may be related to the experimentally observed "intrinsic" critical velocities is discussed.

Part II consists of a semi-classical investigation of rotonquantized vortex line interactions. An essentially classical model is used for the collision and the behavior of the roton in the vortex field is investigated in detail. From this model it is possible to derive the HVBK mutual friction terms that appear in the phenomenalogical equations of motion for rotating liquid He II. Estimates of the Hall and Vinen B and B' coefficients are in good agreement with experiments. The claim is made that the theory does not contain any arbitrary adjustable parameters.

Topological strings, double affine Hecke algebras, and exceptional knot homology

In this thesis, we consider two main subjects: refined, composite invariants and exceptional knot homologies of torus knots. The main technical tools are double affine Hecke algebras ("DAHA") and various insights from topological string theory.

In particular, we define and study the composite DAHA-superpolynomials of torus knots, which depend on pairs of Young diagrams and generalize the composite HOMFLY-PT polynomials from the full HOMFLY-PT skein of the annulus. We also describe a rich structure of differentials that act on homological knot invariants for exceptional groups. These follow from the physics of BPS states and the adjacencies/spectra of singularities associated with Landau-Ginzburg potentials. At the end, we construct two DAHA-hyperpolynomials which are closely related to the Deligne-Gross exceptional series of root systems.

In addition to these main themes, we also provide new results connecting DAHA-Jones polynomials to quantum torus knot invariants for Cartan types A and D, as well as the first appearance of quantum E6 knot invariants in the literature.

I. Current commutators in quantum electrodynamics. II. Electromagnetic mass differences of the pseudoscalar meson and baryon octets

This thesis is in two parts. In the first section, the operator structure of the singular terms in the equal-time commutator of space and time components of the electromagnetic current is investigated in perturbation theory by establishing a connection with Feynman diagrams. It is made very plausible that the singular term is a c number. Some remarks are made about the same problem in the electrodynamics of a spinless particle.

In the second part, an SU(3) symmetric multi-channel calculation of the electromagnetic mass differences in the pseudoscalar meson and baryon octets is carried out with an attempt to include some of the physics of the crossed (pair annihilation) channel along the lines of the recent work by Ball and Zachariasen. The importance of the tensor meson Regge trajectories is emphasized. The agreement with experiment is poor for the isospin one mass differences, but excellent for those with isospin two.

Treewidth: theory and applications to computer science

This report is an introduction to the concept of treewidth, a property of graphs that has important implications in algorithms. Some basic concepts of graph theory are presented in the first chapter for those readers that are not familiar with the notation. In Chapter 2, the definition of treewidth and some different ways of characterizing it are explained. The last two chapters focus on the algorithmic implications of treewidth, which are very relevant in Computer Science. An algorithm to compute the treewidth of a graph is presented and its result can be later applied to many other problems in graph theory, like those introduced in the last chapter.

Distribution theory and fundamental solutions of differential operators

The objective of this dissertation is to study the theory of distributions and some of its applications. Certain concepts which we would include in the theory of distributions nowadays have been widely used in several fields of mathematics and physics. It was Dirac who first introduced the delta function as we know it, in an attempt to keep a convenient notation in his works in quantum mechanics. Their work contributed to open a new path in mathematics, as new objects, similar to functions but not of their same nature, were being used systematically. Distributions are believed to have been first formally introduced by the Soviet mathematician Sergei Sobolev and by Laurent Schwartz. The aim of this project is to show how distribution theory can be used to obtain what we call fundamental solutions of partial differential equations.

Control theory and systems biology

Presenting a control-theoretic treatment of stoichiometric systems, ... local parametric sensitivity analysis, the two approaches yield identical results. ...