Identification of a cell population model for algae growth processes

The growth process of a Chlamydomonas reinhardtii cell population is modelled with experimental data obtained in a batch reactor. To describe the growth process of this culture, the Droop model, extended by cell population balance model, is considered. On the basis of available measurements and the mathematical model, an optimization problem is defined in order to determine the kinetic parameter values for the growth functions of the Droop model and the cell division parameters of the cell population balance model

The effects of noise on binocular rivalry waves: a stochastic neural field model

We analyse the effects of extrinsic noise on traveling waves of visual perception in a competitive neural field model of binocular rivalry. The model consists of two one-dimensional excitatory neural fields, whose activity variables represent the responses to left-eye and right-eye stimuli, respectively. The two networks mutually inhibit each other, and slow adaptation is incorporated into the model by taking the network connections to exhibit synaptic depression. We first show how, in the absence of any noise, the system supports a propagating composite wave consisting of an invading activity front in one network co-moving with a retreating front in the other network. Using a separation of time scales and perturbation methods previously developed for stochastic reaction-diffusion equations, we then show how multiplicative noise in the activity variables leads to a diffusive–like displacement (wandering) of the composite wave from its uniformly translating position at long time scales, and fluctuations in the wave profile around its instantaneous position at short time scales. The multiplicative noise also renormalizes the mean speed of the wave. We use our analysis to calculate the first passage time distribution for a stochastic rivalry wave to travel a fixed distance, which we find to be given by an inverse Gaussian. Finally, we investigate the effects of noise in the depression variables, which under an adiabatic approximation leads to quenched disorder in the neural fields during propagation of a wave

Nonlinear Systems

The editors of this book have incorporated contributions from a diverse group of leading researchers in the field of nonlinear systems. To enrich the scope of the content, this book contains a valuable selection of works on fractional differential equations.The book aims to provide an overview of the current knowledge on nonlinear systems and some aspects of fractional calculus. The main subject areas are divided into two theoretical and applied sections. Nonlinear systems are useful for researchers in mathematics, applied mathematics, and physics, as well as graduate students who are studying these systems with reference to their theory and application. This book is also an ideal complement to the specific literature on engineering, biology, health science, and other applied science areas. The opportunity given by IntechOpen to offer this book under the open access system contributes to disseminating the field of nonlinear systems to a wide range of researchers

Nonlinear Model Predictive Control for Gas Antisolvent Recrystallization Process

학위논문(석사)--서울대학교 대학원 :공과대학 화학생물공학부,2013. 2. 이종민.Crystallization techniques have been played an important role for several decades in producing various chemical products such as polymers, dyes, pharmaceuticals, and explosives. It is also essentially used in separation and purification stages of petrochemical and fine-chemical industries. Conventional crystallization processes, however, have practical problems in that toxic waste solvent streams are inevitably produced in the process and some substances are contaminated with the solvent, deteriorating the purity. In this reason, novel crystallization processes using supercritical fluids have recently attracted much attention. They are environmentally acceptable due to the use of benign solution such as CO2, applicable to various solutes, and operated at mild conditions, 25℃ and 5-100 bar. These include rapid expansion of supercritical solution (RESS), gas antisolvent (GAS) process, and particles from gas-saturated solutions (PGSS). It is well known that GAS crystallization process attains a very rapid, essentially uniform and very high supersaturation upon reduction of the solid solubility in its solution with dissolution of antisolvent CO2. This owes to the two way mass transfer of CO2 and solvent, for dissolution of CO2 and evaporation of solvent, respectively. This facilitates uniform nucleation and almost instantaneous crystallization, which make the antisolvent crystallization a unique process resulting in the formation of ultra-fine particles with a narrow particle size distribution and controlled morphology. In this work, a dynamic model for GAS process is presented and control approach to obtain a desired particle size distribution (PSD) is proposed. At first, a mathematical model from a population balance model (PBM) is developed to describe PSD of GAS process. The developed GAS model consists of a partial differential equation (PDE), a set of ordinary differential equations (ODE), and algebraic equations associated with it. Thus, it requires a numerical discretization method to solve the PDE. A high resolution (HR) scheme is presented since it is rather simple to implement and more accurate than other discretization methods. Simulation results show the effect of CO2 addition rate on the final particle size distribution in the process. Control issues in GAS processes are quite challenging since the system is highly nonlinear and includes complex crystallization kinetics, nucleation and growth. Researchers have investigated the control of liquid antisolvent crystallization process to find optimal input profile, but the control for gas antisolvnet process has not been much tried yet. It is generally more difficult to control GAS process than liquid antisolvent process since the liquid-vapor phase equilibrium should be considered in the system model. A nonlinear model predictive control (MPC) strategy is proposed to control the particle size distribution of GAS process. Linear MPC, successive linearized MPC are applied to the system and the control results are compared.Abstract i 1. Introduction 1 1.1 Crystallization process in industry 1 1.2 Crystallization mechanism 2 1.3 Crystallization techniques using supercritical fluids 5 1.3.1 Rapid expansion of supercritical solutions (RESS) 5 1.3.2 Gas antisolvent process (GAS) 7 1.3.3 Particles from gas-saturated solutions (PGSS) 9 1.4 Control issues for crystallization process 10 1.5 Outline of the thesis 13 2. Experiment 14 2.1 Materials and equipments 15 2.2 Experimental results 18 3. Modeling and Simulation for GAS process 24 3.1 Population balance model 24 3.2 Mathematical model for GAS process 27 3.3 High resolution method for solving PDE 32 3.4 Simulation results 37 4. Nonlinear Model Predictive Control for GAS Process 42 4.1 Model predictive control algorithm 44 4.2 MPC results of GAS process 49 5. Concluding Remarks 54 Bibliography 56Maste

Modeling of Carbon Black Fragmentation During High‐Intensity Dry Mixing Using the Population Balance Equation and the Discrete Element Method

A complex interaction between the process design and the properties of carbon black (CB) during dry mixing of cathode material influences the microstructure and thus the performance of the Li-ion battery. The description of these interactions by means of a coupling of the mixing process simulation and the fragmentation of CB is the focus of this work. The discrete element method provides information about the frequency and intensity of the stress. The change of the CB size distribution is done by the population balance equation. The material strength as well as the fracture behavior are represented with simple models. The calibration of the model parameters is performed using the Nelder–Mead algorithm. The calibrated models provide good agreement with the measurements of the size distributions from experimental investigations. Transfer of the calibrated parameters to other process settings is possible and provides good agreement in some cases. Recalibration of the fracture behavior improves the accuracy of the model so that it can be used as a predictive tool

Mechanical fluidity of fully suspended biological cells

Mechanical characteristics of single biological cells are used to identify and possibly leverage interesting differences among cells or cell populations. Fluidity---hysteresivity normalized to the extremes of an elastic solid or a viscous liquid---can be extracted from, and compared among, multiple rheological measurements of cells: creep compliance vs. time, complex modulus vs. frequency, and phase lag vs. frequency. With multiple strategies available for acquisition of this nondimensional property, fluidity may serve as a useful and robust parameter for distinguishing cell populations, and for understanding the physical origins of deformability in soft matter. Here, for three disparate eukaryotic cell types deformed in the suspended state via optical stretching, we examine the dependence of fluidity on chemical and environmental influences around a time scale of 1 s. We find that fluidity estimates are consistent in the time and the frequency domains under a structural damping (power-law or fractional derivative)model, but not under an equivalent-complexity lumpedcomponent (spring-dashpot) model; the latter predicts spurious time constants. Although fluidity is suppressed by chemical crosslinking, we find that adenosine triphosphate (ATP) depletion in the cell does not measurably alter the parameter, and thus conclude that active ATP-driven events are not a crucial enabler of fluidity during linear viscoelastic deformation of a suspended cell. Finally, by using the capacity of optical stretching to produce near-instantaneous increases in cell temperature, we establish that fluidity increases with temperature---now measured in a fully suspended, sortable cell without the complicating factor of cell-substratum adhesion

Vegetation responses to variations in climate: A combined ordinary differential equation and sequential Monte Carlo estimation approach

Vegetation responses to variation in climate are a current research priority in the context of accelerated shifts generated by climate change. However, the interactions between environmental and biological factors still represent one of the largest uncertainties in projections of future scenarios, since the relationship between drivers and ecosystem responses has a complex and nonlinear nature. We aimed to develop a model to study the vegetation’s primary productivity dynamic response to temporal variations in climatic conditions as measured by rainfall, temperature and radiation. Thus, we propose a new way to estimate the vegetation response to climate via a non-autonomous version of a classical growth curve, with a time-varying growth rate and carrying capacity parameters according to climate variables. With a Sequential Monte Carlo Estimation to account for complexities in the climate-vegetation relationship to minimize the number of parameters. The model was applied to six key sites identified in a previous study, consisting of different arid and semiarid rangelands from North Patagonia, Argentina. For each site, we selected the time series of MODIS NDVI, and climate data from ERA5 Copernicus hourly reanalysis from 2000 to 2021. After calculating the time series of the a posteriori distribution of parameters, we analyzed the explained capacity of the model in terms of the linear coefficient of determination and the parameters distribution variation. Results showed that most rangelands recorded changes in their sensitivity over time to climatic factors, but vegetation responses were heterogeneous and influenced by different drivers. Differences in this climate-vegetation relationship were recorded among different cases: (1) a marginal and decreasing sensitivity to temperature and radiation, respectively, but a high sensitivity to water availability; (2) high and increasing sensitivity to temperature and water availability, respectively; and (3) a case with an abrupt shift in vegetation dynamics driven by a progressively decreasing sensitivity to water availability, without any changes in the sensitivity either to temperature or radiation. Finally, we also found that the time scale, in which the ecosystem integrated the rainfall phenomenon in terms of the width of the window function used to convolve the rainfall series into a water availability variable, was also variable in time. This approach allows us to estimate the connection degree between ecosystem productivity and climatic variables. The capacity of the model to identify changes over time in the vegetation-climate relationship might inform decision-makers about ecological transitions and the differential impact of climatic drivers on ecosystems.Estación Experimental Agropecuaria BarilocheFil: Bruzzone, Octavio Augusto. Instituto Nacional de Tecnología Agropecuaria (INTA). Estación Experimental Agropecuaria Bariloche; ArgentinaFil: Bruzzone, Octavio Augusto. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Instituto de Investigaciones Forestales y Agropecuarias Bariloche; ArgentinaFil: Perri, Daiana Vanesa. Instituto Nacional de Tecnologia Agropecuaria (INTA). Estación Experimental Agropecuaria Bariloche. Área de Recursos Naturales; ArgentinaFil: Perri, Daiana Vanesa. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Instituto de Investigaciones Forestales y Agropecuarias Bariloche; ArgentinaFil: Easdale, Marcos Horacio. Instituto Nacional de Tecnologia Agropecuaria (INTA). Estación Experimental Agropecuaria Bariloche. Área de Recursos Naturales; ArgentinaFil: Easdale, Marcos Horacio. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Instituto de Investigaciones Forestales y Agropecuarias Bariloche; Argentin

Complementarity of Spike- and Rate-Based Dynamics of Neural Systems

Relationships between spiking-neuron and rate-based approaches to the dynamics of neural assemblies are explored by analyzing a model system that can be treated by both methods, with the rate-based method further averaged over multiple neurons to give a neural-field approach. The system consists of a chain of neurons, each with simple spiking dynamics that has a known rate-based equivalent. The neurons are linked by propagating activity that is described in terms of a spatial interaction strength with temporal delays that reflect distances between neurons; feedback via a separate delay loop is also included because such loops also exist in real brains. These interactions are described using a spatiotemporal coupling function that can carry either spikes or rates to provide coupling between neurons. Numerical simulation of corresponding spike- and rate-based methods with these compatible couplings then allows direct comparison between the dynamics arising from these approaches. The rate-based dynamics can reproduce two different forms of oscillation that are present in the spike-based model: spiking rates of individual neurons and network-induced modulations of spiking rate that occur if network interactions are sufficiently strong. Depending on conditions either mode of oscillation can dominate the spike-based dynamics and in some situations, particularly when the ratio of the frequencies of these two modes is integer or half-integer, the two can both be present and interact with each other