The effects of physiologically plausible connectivity structure on local and global dynamics in large scale brain models.

Functionally relevant large scale brain dynamics operates within the framework imposed by anatomical connectivity and time delays due to finite transmission speeds. To gain insight on the reliability and comparability of large scale brain network simulations, we investigate the effects of variations in the anatomical connectivity. Two different sets of detailed global connectivity structures are explored, the first extracted from the CoCoMac database and rescaled to the spatial extent of the human brain, the second derived from white-matter tractography applied to diffusion spectrum imaging (DSI) for a human subject. We use the combination of graph theoretical measures of the connection matrices and numerical simulations to explicate the importance of both connectivity strength and delays in shaping dynamic behaviour. Our results demonstrate that the brain dynamics derived from the CoCoMac database are more complex and biologically more realistic than the one based on the DSI database. We propose that the reason for this difference is the absence of directed weights in the DSI connectivity matrix.

Spatiotemporal order out of noise

Experimental observations of self-organized behavior arising out of noise are also described, and details on the numerical algorithms needed in the computer simulation of these problems are given.

Algebraic decay of velocity fluctuations in a confined fluid

Computer simulations of a colloidal particle suspended in a fluid confined by rigid walls show that, at long times, the velocity correlation function decays with a negative algebraic tail. The exponent depends on the confining geometry, rather than the spatial dimensionality. We can account for the tail by using a simple mode-coupling theory which exploits the fact that the sound wave generated by a moving particle becomes diffusive.

Spatiotemporal order out of noise

Experimental observations of self-organized behavior arising out of noise are also described, and details on the numerical algorithms needed in the computer simulation of these problems are given.

Optical probing of sodium dynamics in neurons and astrocytes.

Changes in intracellular Na(+) concentration underlie essential neurobiological processes, but few reliable tools exist for their measurement. Here we characterize a new synthetic Na(+)-sensitive fluorescent dye, Asante Natrium Green (ANG), with unique properties. This indicator was excitable in the visible spectrum and by two-photon illumination, suffered little photobleaching and located to the cytosol were it remained for long durations without noticeable unwanted effects on basic cell properties. When used in brain tissue, ANG yielded a bright fluorescent signal during physiological Na(+) responses both in neurons and astrocytes. Synchronous electrophysiological and fluorometric recordings showed that ANG produced accurate Na(+) measurement in situ. This new Na(+) indicator opens innovative ways of probing neuronal circuits.

Short-time dynamics of colloidal suspensions in confined geometries

We analyze the short-time dynamical behavior of a colloidal suspension in a confined geometry. We analyze the relevant dynamical response of the solvent, and derive the temporal behavior of the velocity autocorrelation function, which exhibits an asymptotic negative algebraic decay. We are able to compare quantitatively with theoretical expressions, and analyze the effects of confinement on the diffusive behavior of the suspension.

Performance Analysis of Two Quantum Reaction Dynamics Codes: Time-Dependent and Time-Independent Strategies

The computer simulation of reaction dynamics has nowadays reached a remarkable degree of accuracy. Triatomic elementary reactions are rigorously studied with great detail on a straightforward basis using a considerable variety of Quantum Dynamics computational tools available to the scientific community. In our contribution we compare the performance of two quantum scattering codes in the computation of reaction cross sections of a triatomic benchmark reaction such as the gas phase reaction Ne + H2+ %12. NeH++ H. The computational codes are selected as representative of time-dependent (Real Wave Packet [ ]) and time-independent (ABC [ ]) methodologies. The main conclusion to be drawn from our study is that both strategies are, to a great extent, not competing but rather complementary. While time-dependent calculations advantages with respect to the energy range that can be covered in a single simulation, time-independent approaches offer much more detailed information from each single energy calculation. Further details such as the calculation of reactivity at very low collision energies or the computational effort related to account for the Coriolis couplings are analyzed in this paper.

From caging to rouse dynamics in polymer melts with intramolecular barriers: a critical test of the mode coupling theory

By means of computer simulations and solution of the equations of the mode coupling theory (MCT),we investigate the role of the intramolecular barriers on several dynamic aspects of nonentangled polymers. The investigated dynamic range extends from the caging regime characteristic of glass-formers to the relaxation of the chain Rouse modes. We review our recent work on this question,provide new results, and critically discuss the limitations of the theory. Solutions of the MCT for the structural relaxation reproduce qualitative trends of simulations for weak and moderate barriers. However, a progressive discrepancy is revealed as the limit of stiff chains is approached. This dis-agreement does not seem related with dynamic heterogeneities, which indeed are not enhanced by increasing barrier strength. It is not connected either with the breakdown of the convolution approximation for three-point static correlations, which retains its validity for stiff chains. These findings suggest the need of an improvement of the MCT equations for polymer melts. Concerning the relaxation of the chain degrees of freedom, MCT provides a microscopic basis for time scales from chain reorientation down to the caging regime. It rationalizes, from first principles, the observed deviations from the Rouse model on increasing the barrier strength. These include anomalous scaling of relaxation times, long-time plateaux, and nonmonotonous wavelength dependence of the mode correlators.

Synchronization of symmetric chaotic systems

This paper contains a study of the synchronization by homogeneous nonlinear driving of systems that are symmetric in phase space. The main consequence of this symmetry is the ability of the response to synchronize in more than just one way to the driving systems. These different forms of synchronization are to be understood as generalized synchronization states in which the motions of drive and response are in complete correlation, but the phase space distance between them does not converge to zero. In this case the synchronization phenomenon becomes enriched because there is multistability. As a consequence, there appear multiple basins of attraction and special responses to external noise. It is shown, by means of a computer simulation of various nonlinear systems, that: (i) the decay to the generalized synchronization states is exponential, (ii) the basins of attraction are symmetric, usually complicated, frequently fractal, and robust under the changes in the parameters, and (iii) the effect of external noise is to weaken the synchronization, and in some cases to produce jumps between the various synchronization states available

Chaotic systems with a null conditional Lyapunov exponent under nonlinear driving.

Control of a chaotic system by homogeneous nonlinear driving, when a conditional Lyapunov exponent is zero, may give rise to special and interesting synchronizationlike behaviors in which the response evolves in perfect correlation with the drive. Among them, there are the amplification of the drive attractor and the shift of it to a different region of phase space. In this paper, these synchronizationlike behaviors are discussed, and demonstrated by computer simulation of the Lorentz model [E. N. Lorenz, J. Atmos. Sci. 20 130 (1963)] and the double scroll [T. Matsumoto, L. O. Chua, and M. Komuro, IEEE Trans. CAS CAS-32, 798 (1985)].

Simulation of Boundary Layers and Heat Transfer in the Entrance Region of Pipes

The study of fluid flow in pipes is one of the main topic of interest for engineers in industries. In this thesis, an effort is made to study the boundary layers formed near the wall of the pipe and how it behaves as a resistance to heat transfer. Before few decades, the scientists used to derive the analytical and empirical results by hand as there were limited means available to solve the complex fluid flow phenomena. Due to the increase in technology, now it has been practically possible to understand and analyze the actual fluid flow in any type of geometry. Several methodologies have been used in the past to analyze the boundary layer equations and to derive the expression for heat transfer. An integral relation approach is used for the analytical solution of the boundary layer equations and is compared with the FLUENT simulations for the laminar case. Law of the wall approach is used to derive the empirical correlation between dimensionless numbers and is then compared with the results from FLUENT for the turbulent case. In this thesis, different approaches like analytical, empirical and numerical are compared for the same set of fluid flow equations.

Theoretical Analysis and Simulations of Vertically Vibrated Granular Materials

The dynamical properties ofshaken granular materials are important in many industrial applications where the shaking is used to mix, segregate and transport them. In this work asystematic, large scale simulation study has been performed to investigate the rheology of dense granular media, in the presence of gas, in a three dimensional vertical cylinder filled with glass balls. The base wall of the cylinder is subjected to sinusoidal oscillation in the vertical direction. The viscoelastic behavior of glass balls during a collision, have been studied experimentally using a modified Newton's Cradle device. By analyzing the results of the measurements, using numerical model based on finite element method, the viscous damping coefficient was determinedfor the glass balls. To obtain detailed information about the interparticle interactions in a shaker, a simplified model for collision between particles of a granular material was proposed. In order to simulate the flow of surrounding gas, a formulation of the equations for fluid flow in a porous medium including particle forces was proposed. These equations are solved with Large Eddy Simulation (LES) technique using a subgrid-model originally proposed for compressible turbulent flows. For a pentagonal prism-shaped container under vertical vibrations, the results show that oscillon type structures were formed. Oscillons are highly localized particle-like excitations of the granular layer. This self-sustaining state was named by analogy with its closest large-scale analogy, the soliton, which was first documented by J.S. Russell in 1834. The results which has been reportedbyBordbar and Zamankhan(2005b)also show that slightly revised fluctuation-dissipation theorem might apply to shaken sand, which appears to be asystem far from equilibrium and could exhibit strong spatial and temporal variations in quantities such as density and local particle velocity. In this light, hydrodynamic type continuum equations were presented for describing the deformation and flow of dense gas-particle mixtures. The constitutive equation used for the stress tensor provides an effective viscosity with a liquid-like character at low shear rates and a gaseous-like behavior at high shear rates. The numerical solutions were obtained for the aforementioned hydrodynamic equations for predicting the flow dynamics ofdense mixture of gas and particles in vertical cylindrical containers. For a heptagonal prism shaped container under vertical vibrations, the model results were found to predict bubbling behavior analogous to those observed experimentally. This bubbling behavior may be explained by the unusual gas pressure distribution found in the bed. In addition, oscillon type structures were found to be formed using a vertically vibrated, pentagonal prism shaped container in agreement with computer simulation results. These observations suggest that the pressure distribution plays a key rolein deformation and flow of dense mixtures of gas and particles under vertical vibrations. The present models provide greater insight toward the explanation of poorly understood hydrodynamic phenomena in the field of granular flows and dense gas-particle mixtures. The models can be generalized to investigate the granular material-container wall interactions which would be an issue of high interests in the industrial applications. By following this approach ideal processing conditions and powder transport can be created in industrial systems.

Control and Simulation of Batch Crystallization

Concerning process control of batch cooling crystallization the present work focused on the cooling profile and seeding technique. Secondly, the influence of additives on batch-wise precipitation process was investigated. Moreover, a Computational Fluid Dynamics (CFD) model for simulation of controlled batch cooling crystallization was developed. A novel cooling model to control supersaturation level during batch-wise cooling crystallization was introduced. The crystallization kinetics together with operating conditions, i.e. seed loading, cooling rate and batch time, were taken into account in the model. Especially, the supersaturation- and suspension density- dependent secondary nucleation was included in the model. The interaction between the operating conditions and their influence on the control target, i.e. the constant level of supersaturation, were studied with the aid of a numerical solution for the cooling model. Further, the batch cooling crystallization was simulated with the ideal mixing model and CFD model. The moment transformation of the population balance, together with the mass and heat balances, were solved numerically in the simulation. In order to clarify a relationship betweenthe operating conditions and product sizes, a system chart was developed for anideal mixing condition. The utilization of the system chart to determine the appropriate operating condition to meet a required product size was introduced. With CFD simulation, batch crystallization, operated following a specified coolingmode, was studied in the crystallizers having different geometries and scales. The introduced cooling model and simulation results were verified experimentallyfor potassium dihydrogen phosphate (KDP) and the novelties of the proposed control policies were demonstrated using potassium sulfate by comparing with the published results in the literature. The study on the batch-wise precipitation showed that immiscible additives could promote the agglomeration of a derivative of benzoic acid, which facilitated the filterability of the crystal product.

Using Pareto optimality to explore the topology and dynamics of the human connectome.

Graph theory has provided a key mathematical framework to analyse the architecture of human brain networks. This architecture embodies an inherently complex relationship between connection topology, the spatial arrangement of network elements, and the resulting network cost and functional performance. An exploration of these interacting factors and driving forces may reveal salient network features that are critically important for shaping and constraining the brain's topological organization and its evolvability. Several studies have pointed to an economic balance between network cost and network efficiency with networks organized in an 'economical' small-world favouring high communication efficiency at a low wiring cost. In this study, we define and explore a network morphospace in order to characterize different aspects of communication efficiency in human brain networks. Using a multi-objective evolutionary approach that approximates a Pareto-optimal set within the morphospace, we investigate the capacity of anatomical brain networks to evolve towards topologies that exhibit optimal information processing features while preserving network cost. This approach allows us to investigate network topologies that emerge under specific selection pressures, thus providing some insight into the selectional forces that may have shaped the network architecture of existing human brains.

Analysis of flow dynamics in right ventricular outflow tract.

BACKGROUND: The mechanism behind early graft failure after right ventricular outflow tract (RVOT) reconstruction is not fully understood. Our aim was to establish a three-dimensional computational fluid dynamics (CFD) model of RVOT to investigate the hemodynamic conditions that may trigger the development of intimal hyperplasia and arteriosclerosis. METHODS: Pressure, flow, and diameter at the RVOT, pulmonary artery (PA), bifurcation of the PA, and left and right PAs were measured in 10 normal pigs with a mean weight of 24.8 ± 0.78 kg. Data obtained from the experimental scenario were used for CFD simulation of pressure, flow, and shear stress profile from the RVOT to the left and right PAs. RESULTS: Using experimental data, a CFD model was obtained for 2.0 and 2.5-L/min pulsatile inflow profiles. In both velocity profiles, time and space averaged in the low-shear stress profile range from 0-6.0 Pa at the pulmonary trunk, its bifurcation, and at the openings of both PAs. These low-shear stress areas were accompanied to high-pressure regions 14.0-20.0 mm Hg (1866.2-2666 Pa). Flow analysis revealed a turbulent flow at the PA bifurcation and ostia of both PAs. CONCLUSIONS: Identified local low-shear stress, high pressure, and turbulent flow correspond to a well-defined trigger pattern for the development of intimal hyperplasia and arteriosclerosis. As such, this real-time three-dimensional CFD model may in the future serve as a tool for the planning of RVOT reconstruction, its analysis, and prediction of outcome.