Entropic transport: kinetics, scaling, and control mechanisms

We show that transport in the presence of entropic barriers exhibits peculiar characteristics which makes it distinctly different from that occurring through energy barriers. The constrained dynamics yields a scaling regime for the particle current and the diffusion coefficient in terms of the ratio between the work done to the particles and available thermal energy. This interesting property, genuine to the entropic nature of the barriers, can be utilized to effectively control transport through quasi-one-dimensional structures in which irregularities or tortuosity of the boundaries cause entropic effects. The accuracy of the kinetic description has been corroborated by simulations. Applications to different dynamic situations involving entropic barriers are outlined.

Dynamical sectors of a relativistic two particle model

We reconsider a model of two relativistic particles interacting via a multiplicative potential, as an example of a simple dynamical system with sectors, or branches, with different dynamics and degrees of freedom. The presence or absence of sectors depends on the values of rest masses. Some aspects of the canonical quantization are described. The model could be interpreted as a bigravity model in one dimension.

Problems of allometric scaling analysis: examples from mammalian reproductive biology.

Biological scaling analyses employing the widely used bivariate allometric model are beset by at least four interacting problems: (1) choice of an appropriate best-fit line with due attention to the influence of outliers; (2) objective recognition of divergent subsets in the data (allometric grades); (3) potential restrictions on statistical independence resulting from phylogenetic inertia; and (4) the need for extreme caution in inferring causation from correlation. A new non-parametric line-fitting technique has been developed that eliminates requirements for normality of distribution, greatly reduces the influence of outliers and permits objective recognition of grade shifts in substantial datasets. This technique is applied in scaling analyses of mammalian gestation periods and of neonatal body mass in primates. These analyses feed into a re-examination, conducted with partial correlation analysis, of the maternal energy hypothesis relating to mammalian brain evolution, which suggests links between body size and brain size in neonates and adults, gestation period and basal metabolic rate. Much has been made of the potential problem of phylogenetic inertia as a confounding factor in scaling analyses. However, this problem may be less severe than suspected earlier because nested analyses of variance conducted on residual variation (rather than on raw values) reveals that there is considerable variance at low taxonomic levels. In fact, limited divergence in body size between closely related species is one of the prime examples of phylogenetic inertia. One common approach to eliminating perceived problems of phylogenetic inertia in allometric analyses has been calculation of 'independent contrast values'. It is demonstrated that the reasoning behind this approach is flawed in several ways. Calculation of contrast values for closely related species of similar body size is, in fact, highly questionable, particularly when there are major deviations from the best-fit line for the scaling relationship under scrutiny.

Scaling behavior of random knots.

Using numerical simulations we investigate how overall dimensions of random knots scale with their length. We demonstrate that when closed non-self-avoiding random trajectories are divided into groups consisting of individual knot types, then each such group shows the scaling exponent of approximately 0.588 that is typical for self-avoiding walks. However, when all generated knots are grouped together, their scaling exponent becomes equal to 0.5 (as in non-self-avoiding random walks). We explain here this apparent paradox. We introduce the notion of the equilibrium length of individual types of knots and show its correlation with the length of ideal geometric representations of knots. We also demonstrate that overall dimensions of random knots with a given chain length follow the same order as dimensions of ideal geometric representations of knots.

ADVANCED NUMERICAL METHODS FOR SIMULATING MICROBUBBLE IN AN AERATED MIXING TANK

Fluid mixing in mechanically agitated tanks is one of the major unit operations in many industries. Bubbly flows have been of interest among researchers in physics, medicine, chemistry and technology over the centuries. The aim of this thesis is to use advanced numerical methods for simulating microbubble in an aerated mixing tank. Main components of the mixing tank are a cylindrical vessel, a rotating Rushton turbine and the air nozzle. The objective of Computational Fluid Dynamics (CFD) is to predict fluid flow, heat transfer, mass transfer and chemical reactions. The CFD simulations of a turbulent bubbly flow are carried out in a cylindrical mixing tank using large eddy simulation (LES) and volume of fluid (VOF) method. The Rushton turbine induced flow is modeled by using a sliding mesh method. Numerical results are used to describe the bubbly flows in highly complex liquid flow. Some of the experimental works related to turbulent bubbly flow in a mixing tank are briefly reported. Numerical simulations are needed to complete and interpret the results of the experimental work. Information given by numerical simulations has a major role in designing and scaling-up mixing tanks. The results of this work have been reported in the following scientific articles: ·Honkanen M., Koohestany A., Hatunen T., Saarenrinne P., Zamankhan P., Large eddy simulations and PIV experiments of a two-phase air-water mixer, in Proceedings of ASME Fluids Engineering Summer Conference (2005). ·Honkanen M., Koohestany A., Hatunen T., Saarenrinne P., Zamankhan P., Dynamical States of Bubbling in an Aerated Stirring Tank, submitted to J. Computational Physics.

Fluid dynamical prediction of changed v1-flow at energies available at the CERN Large Hadron Collider

Substantial collective flow is observed in collisions between lead nuclei at Large Hadron Collider (LHC) as evidenced by the azimuthal correlations in the transverse momentum distributions of the produced particles. Our calculations indicate that the global v1-flow, which at RHIC peaked at negative rapidities (named third flow component or antiflow), now at LHC is going to turn toward forward rapidities (to the same side and direction as the projectile residue). Potentially this can provide a sensitive barometer to estimate the pressure and transport properties of the quark-gluon plasma. Our calculations also take into account the initial state center-of-mass rapidity fluctuations, and demonstrate that these are crucial for v1 simulations. In order to better study the transverse momentum flow dependence we suggest a new"symmetrized" vS1(pt) function, and we also propose a new method to disentangle global v1 flow from the contribution generated by the random fluctuations in the initial state. This will enhance the possibilities of studying the collective Global v1 flow both at the STAR Beam Energy Scan program and at LHC.

Nonlinear principal and canonical directions from continuous extensions of multidimensional scaling

A continuous random variable is expanded as a sum of a sequence of uncorrelated random variables. These variables are principal dimensions in continuous scaling on a distance function, as an extension of classic scaling on a distance matrix. For a particular distance, these dimensions are principal components. Then some properties are studied and an inequality is obtained. Diagonal expansions are considered from the same continuous scaling point of view, by means of the chi-square distance. The geometric dimension of a bivariate distribution is defined and illustrated with copulas. It is shown that the dimension can have the power of continuum.

Full instability behavior of N-dimensional dynamical systems with a one-directional nonlinear vector field

We show how certain N-dimensional dynamical systems are able to exploit the full instability capabilities of their fixed points to do Hopf bifurcations and how such a behavior produces complex time evolutions based on the nonlinear combination of the oscillation modes that emerged from these bifurcations. For really different oscillation frequencies, the evolutions describe robust wave form structures, usually periodic, in which selfsimilarity with respect to both the time scale and system dimension is clearly appreciated. For closer frequencies, the evolution signals usually appear irregular but are still based on the repetition of complex wave form structures. The study is developed by considering vector fields with a scalar-valued nonlinear function of a single variable that is a linear combination of the N dynamical variables. In this case, the linear stability analysis can be used to design N-dimensional systems in which the fixed points of a saddle-node pair experience up to N21 Hopf bifurcations with preselected oscillation frequencies. The secondary processes occurring in the phase region where the variety of limit cycles appear may be rather complex and difficult to characterize, but they produce the nonlinear mixing of oscillation modes with relatively generic features

On Undecidable Dynamical Properties of Reversible One-Dimensional Cellular Automata

Cellular automata are models for massively parallel computation. A cellular automaton consists of cells which are arranged in some kind of regular lattice and a local update rule which updates the state of each cell according to the states of the cell's neighbors on each step of the computation. This work focuses on reversible one-dimensional cellular automata in which the cells are arranged in a two-way in_nite line and the computation is reversible, that is, the previous states of the cells can be derived from the current ones. In this work it is shown that several properties of reversible one-dimensional cellular automata are algorithmically undecidable, that is, there exists no algorithm that would tell whether a given cellular automaton has the property or not. It is shown that the tiling problem of Wang tiles remains undecidable even in some very restricted special cases. It follows that it is undecidable whether some given states will always appear in computations by the given cellular automaton. It also follows that a weaker form of expansivity, which is a concept of dynamical systems, is an undecidable property for reversible one-dimensional cellular automata. It is shown that several properties of dynamical systems are undecidable for reversible one-dimensional cellular automata. It shown that sensitivity to initial conditions and topological mixing are undecidable properties. Furthermore, non-sensitive and mixing cellular automata are recursively inseparable. It follows that also chaotic behavior is an undecidable property for reversible one-dimensional cellular automata.

On convergence of transforms based on parabolic scaling

This thesis studies properties of transforms based on parabolic scaling, like Curvelet-, Contourlet-, Shearlet- and Hart-Smith-transform. Essentially, two di erent questions are considered: How these transforms can characterize H older regularity and how non-linear approximation of a piecewise smooth function converges. In study of Hölder regularities, several theorems that relate regularity of a function f : R2 → R to decay properties of its transform are presented. Of particular interest is the case where a function has lower regularity along some line segment than elsewhere. Theorems that give estimates for direction and location of this line, and regularity of the function are presented. Numerical demonstrations suggest also that similar theorems would hold for more general shape of segment of low regularity. Theorems related to uniform and pointwise Hölder regularity are presented as well. Although none of the theorems presented give full characterization of regularity, the su cient and necessary conditions are very similar. Another theme of the thesis is the study of convergence of non-linear M ─term approximation of functions that have discontinuous on some curves and otherwise are smooth. With particular smoothness assumptions, it is well known that squared L2 approximation error is O(M-2(logM)3) for curvelet, shearlet or contourlet bases. Here it is shown that assuming higher smoothness properties, the log-factor can be removed, even if the function still is discontinuous.

Dynamical and structural properties of dendrimer macromolecules

This work is devoted to the study of the dynamical and structural properties of dendrimers. Different approaches were used: analytical theory, computer simulation results and experimental NMR studies. The theory of the relaxation spectrum of dendrimer macromolecules was developed. Relaxation processes which are manifest in the local orientational mobility of dendrimer macromolecules were established and studied in detail. Theoretical results and conclusions were used for experimental studies of carbosilane dendimers.

Hipsometric relationship modeling using data sampled in tree scaling and inventory plots

This work evaluated eight hypsometric models to represent tree height-diameter relationship, using data obtained from the scaling of 118 trees and 25 inventory plots. Residue graphic analysis and percent deviation mean criteria, qui-square test precision, residual standard error between real and estimated heights and the graybill f test were adopted. The identity of the hypsometric models was also verified by applying the F(Ho) test on the plot data grouped to the scaling data. It was concluded that better accuracy can be obtained by using the model prodan, with h and d1,3 data measured in 10 trees by plots grouped into these scaling data measurements of even-aged forest stands.

Challenges in scaling agile software development in offshoring environment

Corporate decision to scale Agile Software development methodologies in offshoring environment has been obstructed due to possible challenges in scaling agile as agile methodologies are regarded to be suitable for small project and co-located team only. Although model such as Agile Scaling Model (ASM) has been developed for scaling Agile with different factors, inabilities of companies to figure out challenges and addressing them lead to failure of project rather than gaining the benefits of using agile methodologies. This failure can be avoided, when scaling agile in IT offshoring environment, by determining key challenges associated in scaling agile in IT offshoring environment and then preparing strategies for addressing those key challenges. These key challenges in scaling agile with IT offshoring environment can be determined by studying issues related with Offshoring and Agile individually and also considering the positive impact of agile methodology in offshoring environment. Then, possible strategies to tackle these key challenges are developed according to the nature of individual challenges and utilizing the benefits of different agile methodologies to address individual situation. Thus, in this thesis, we proposed strategy of using hybrid agile method, which is increasing trend due to adaptive nature of Agile. Determination of the key challenges and possible strategies for tackling those challenges are supported with the survey conducted in the researched organization.