Efficient simulations of tubulin-driven axonal growth

This work concerns efficient and reliable numerical simulations of the dynamic behaviour of a moving-boundary model for tubulin-driven axonal growth. The model is nonlinear and consists of a coupled set of a partial differential equation (PDE) and two ordinary differential equations. The PDE is defined on a computational domain with a moving boundary, which is part of the solution. Numerical simulations based on standard explicit time-stepping methods are too time consuming due to the small time steps required for numerical stability. On the other hand standard implicit schemes are too complex due to the nonlinear equations that needs to be solved in each step. Instead, we propose to use the Peaceman--Rachford splitting scheme combined with temporal and spatial scalings of the model. Simulations based on this scheme have shown to be efficient, accurate, and reliable which makes it possible to evaluate the model, e.g.\ its dependency on biological and physical model parameters. These evaluations show among other things that the initial axon growth is very fast, that the active transport is the dominant reason over diffusion for the growth velocity, and that the polymerization rate in the growth cone does not affect the final axon length.Comment: Authors' accepted version, (post refereeing). The final publication (in Journal of Computational Neuroscience) is available at Springer via http://dx.doi.org/10.1007/s10827-016-0604-

Towards improved 1-D settler modelling : calibration of the Bürger model and case study

Recently, Burger et al. (2011) developed a new 1-D SST model which allows for more realistic predictions of the sludge settling behaviour than traditional 1-D models used to date. However, the addition of a compression function in this new 1-D model complicates the model calibration. This study aims to report advances in the calibration of this novel 1-D model. Data of the evolution of the sludge blanket height during batch settling experiments were collected at different initial solids concentrations. Based on the linear slopes of the batch settling curves the hindered settling velocity functions by Vesilind (1968) and Takacs et al. (1991) were calibrated. Although both settling velocity functions gave a good fit to the experimental data, very large confidence intervals were found for the parameters of the settling velocity by Takacs. Global sensitivity analysis showed that it is not possible to find a unique set of parameter values for the settling function by Takacs based on experimental data of the hindered settling velocity. Subsequently, the calibrated Vesilind settling velocity was implemented in the 1-D model by Burger et al. (2011) and the parameters of the additional compression function were calibrated by fitting the model by Burger et al. (2011) to the batch settling curves. Simulation results showed that while the 1-D model by Takacs et al. (1991) underpredicted the experimental data of sludge blanket heights, the model by Burger et al. (2011) was able to predict the experimental data far more accurately. However, a global sensitivity analysis showed that no unique optimum for the combined set of hindered and compression parameters could be found

Differentiability results and sensitivity calculation for optimal control of incompressible two-phase Navier-Stokes equations with surface tension

We analyze optimal control problems for two-phase Navier-Stokes equations with surface tension. Based on $L_p$-maximal regularity of the underlying linear problem and recent well-posedness results of the problem for sufficiently small data we show the differentiability of the solution with respect to initial and distributed controls for appropriate spaces resulting form the $L_p$-maximal regularity setting. We consider first a formulation where the interface is transformed to a hyperplane. Then we deduce differentiability results for the solution in the physical coordinates. Finally, we state an equivalent Volume-of-Fluid type formulation and use the obtained differentiability results to derive rigorosly the corresponding sensitivity equations of the Volume-of-Fluid type formulation. For objective functionals involving the velocity field or the discontinuous pressure or phase indciator field we derive differentiability results with respect to controls and state formulas for the derivative. The results of the paper form an analytical foundation for stating optimality conditions, justifying the application of derivative based optimization methods and for studying the convergence of discrete sensitivity schemes based on Volume-of-Fluid discretizations for optimal control of two-phase Navier-Stokes equations

Derivative-free Parameter Optimization of Functional Mock-up Units

Representing a physical system with a mathematical model requires knowledge not only about the physical laws governing the dynamics but also about the parameter values of the system. The parameters can sometimes be measured or calculated, however some of them are often difficult or impossible to obtain in these ways. Finding accurate parameter values is crucial for the accuracy of the mathematical model. Estimating the parameters using optimization algorithms which attempt to minimize the error between the response from the mathematical model and the physical system is a common approach for improving the accuracy of the model. Optimization algorithms usually requires information about the derivatives which may not always be available or not be appropriate for estimation which forces the use of derivative-free optimization algorithms. In this paper, we present an implementation of derivative-free optimization algorithms for parameter estimation in the JModelica.org platform. The implementation allows the underlying dynamic system to be represented as a Functional Mock-up Unit (FMU), thus enables parameter estimation of models designed in modeling tools following the standardized interface, the Functional Mock-up Interface (FMI), such as Dymola

Hippocampal CA2 Activity Patterns Change over Time to a Larger Extent than between Spatial Contexts

SummaryThe hippocampal CA2 subregion has a different anatomical connectivity pattern within the entorhino-hippocampal circuit than either the CA1 or CA3 subregion. Yet major differences in the neuronal activity patterns of CA2 compared with the other CA subregions have not been reported. We show that standard spatial and temporal firing patterns of individual hippocampal principal neurons in behaving rats, such as place fields, theta modulation, and phase precession, are also present in CA2, but that the CA2 subregion differs substantially from the other CA subregions in its population coding. CA2 ensembles do not show a persistent code for space or for differences in context. Rather, CA2 activity patterns become progressively dissimilar over time periods of hours to days. The weak coding for a particular context is consistent with recent behavioral evidence that CA2 circuits preferentially support social, emotional, and temporal rather than spatial aspects of memory

Efimov physics from the functional renormalization group

Few-body physics related to the Efimov effect is discussed using the functional renormalization group method. After a short review of renormalization in its modern formulation we apply this formalism to the description of scattering and bound states in few-body systems of identical bosons and distinguishable fermions with two and three components. The Efimov effect leads to a limit cycle in the renormalization group flow. Recently measured three-body loss rates in an ultracold Fermi gas $^6$Li atoms are explained within this framework. We also discuss briefly the relation to the many-body physics of the BCS-BEC crossover for two-component fermions and the formation of a trion phase for the case of three species.Comment: 28 pages, 13 figures, invited contribution to a special issue of "Few-Body Systems" devoted to Efimov physics, published versio