Large-scale Continuum Random Phase Approximation predictions of dipole strength for astrophysical applications

Large-scale calculations of the E1 strength are performed within the random phase approximation (RPA) based on the relativistic point-coupling mean field approach in order to derive the radiative neutron capture cross sections for all nuclei of astrophysical interest. While the coupling to the single-particle continuum is taken into account in an explicit and self-consistent way, additional corrections like the coupling to complex configurations and the temperature and deformation effects are included in a phenomenological way to account for a complete description of the nuclear dynamical problem. It is shown that the resulting E1-strength function based on the PCF1 force is in close agreement with photoabsorption data as well as the available experimental E1 strength data at low energies. For neutron-rich nuclei, as well as light neutron-deficient nuclei, a low-lying so-called pygmy resonance is found systematically in the 5-10 MeV region. The corresponding strength can reach 10% of the giant dipole strength in the neutron-rich region and about 5% in the neutron-deficient region, and is found to be reduced in the vicinity of the shell closures. Finally, the neutron capture reaction rates of neutron-rich nuclei is found to be about 2-5 times larger than those predicted on the basis of the nonrelativistic RPA calculation and about a factor 50 larger than obtained with traditional Lorentzian-type approaches.Comment: 11 pages, 12 figure

Relativistic Continuum Quasiparticle Random Phase Approximation in Spherical Nuclei

We have calculated the strength distributions of the dipole response in spherical nuclei, ranging all over the periodic table. The calculations were performed within two microscopic models: the discretized quasiparticle random phase approximation (QRPA) and the quasiparticle continuum RPA, which takes into account the coupling of the single-particle continuum in an exact way. Pairing correlations are treated with the BCS model. In the calculations, two density functionals were used, namely the functional PC-F1 and the functional DD-PC1. Both are based on relativistic point coupling Lagrangians. It is explicitly shown that this model is capable of reproducing the giant as well as the pygmy dipole resonance for open-shell nuclei in a high level of quantitative agreement with the available experimental observations.Comment: 9 pages, 6 figures, accepted for publication in Phys. Pev.

Computationally efficient solution of mixed integer model predictive control problems via machine learning aided Benders Decomposition

Mixed integer Model Predictive Control (MPC) problems arise in the operation of systems where discrete and continuous decisions must be taken simultaneously to compensate for disturbances. The efficient solution of mixed integer MPC problems requires the computationally efficient and robust online solution of mixed integer optimization problems, which are generally difficult to solve. In this paper, we propose a machine learning-based branch and check Generalized Benders Decomposition algorithm for the efficient solution of such problems. We use machine learning to approximate the effect of the complicating variables on the subproblem by approximating the Benders cuts without solving the subproblem, therefore, alleviating the need to solve the subproblem multiple times. The proposed approach is applied to a mixed integer economic MPC case study on the operation of chemical processes. We show that the proposed algorithm always finds feasible solutions to the optimization problem, given that the mixed integer MPC problem is feasible, and leads to a significant reduction in solution time (up to 97% or 50x) while incurring small error (in the order of 1%) compared to the application of standard and accelerated Generalized Benders Decomposition

Stochastic simulations of the tetracycline operon

<p>Abstract</p> <p>Background</p> <p>The tetracycline operon is a self-regulated system. It is found naturally in bacteria where it confers resistance to antibiotic tetracycline. Because of the performance of the molecular elements of the tetracycline operon, these elements are widely used as parts of synthetic gene networks where the protein production can be efficiently turned on and off in response to the presence or the absence of tetracycline. In this paper, we investigate the dynamics of the tetracycline operon. To this end, we develop a mathematical model guided by experimental findings. Our model consists of biochemical reactions that capture the biomolecular interactions of this intriguing system. Having in mind that small biological systems are subjects to stochasticity, we use a stochastic algorithm to simulate the tetracycline operon behavior. A sensitivity analysis of two critical parameters embodied this system is also performed providing a useful understanding of the function of this system.</p> <p>Results</p> <p>Simulations generate a timeline of biomolecular events that confer resistance to bacteria against tetracycline. We monitor the amounts of intracellular TetR2 and TetA proteins, the two important regulatory and resistance molecules, as a function of intrecellular tetracycline. We find that lack of one of the promoters of the tetracycline operon has no influence on the total behavior of this system inferring that this promoter is not essential for <it>Escherichia coli</it>. Sensitivity analysis with respect to the binding strength of tetracycline to repressor and of repressor to operators suggests that these two parameters play a predominant role in the behavior of the system. The results of the simulations agree well with experimental observations such as tight repression, fast gene expression, induction with tetracycline, and small intracellular TetR2 amounts.</p> <p>Conclusions</p> <p>Computer simulations of the tetracycline operon afford augmented insight into the interplay between its molecular components. They provide useful explanations of how the components and their interactions have evolved to best serve bacteria carrying this operon. Therefore, simulations may assist in designing novel gene network architectures consisting of tetracycline operon components.</p

CH in stellar atmospheres: an extensive linelist

The advent of high-resolution spectrographs and detailed stellar atmosphere modelling has strengthened the need for accurate molecular data. Carbon-enhanced metal-poor (CEMP) stars spectra are interesting objects with which to study transitions from the CH molecule. We combine programs for spectral analysis of molecules and stellar-radiative transfer codes to build an extensive CH linelist, including predissociation broadening as well as newly identified levels. We show examples of strong predissociation CH lines in CEMP stars, and we stress the important role played by the CH features in the Bond-Neff feature depressing the spectra of barium stars by as much as 0.2 magnitudes in the $\lambda=$3000 -- 5500 \AA\ range. Because of the extreme thermodynamic conditions prevailing in stellar atmospheres (compared to the laboratory), molecular transitions with high energy levels can be observed. Stellar spectra can thus be used to constrain and improve molecular data.Comment: 33pages, 15 figures, accepted in A&A external data available at http://www.astro.ulb.ac.be/~spectrotools

Synthesis of feedforward/state feedback controllers for nonlinear processes

A systematic method for synthesizing feedforward/state feedback controllers for a broad class of SISO nonlinear systems with measurable disturbances is presented. Depending on the structural characteristics of the system, the control law can be static or dynamic. The closed-loop system is independent of the measurable disturbances and linear with respect to set point changes. The performance of the proposed control scheme is illustrated through an example of composition control in a system of three CSTR's in series.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/37404/1/690351004_ftp.pd

Dynamic output feedback control of minimum-phase multivariable nonlinear processes

This paper concerns the synthesis of dynamic output feedback controllers for minimum-phase multivariable nonlinear processes with a nonsingular characteristic matrix. State-space controller realizations are derived that induce a linear input/output behavior of general form in the closed-loop system. A combination of input/output linearizing state feedback laws and state observers is employed for the derivation of the controllers. For open-loop stable processes, the process model is used as an open-loop state observer. In the more general case of possible open-loop instability, a reduced-order observer is used based on the forced zero dynamics of the process model. The performance and robustness characteristics of the proposed control methodology are illustrated through simulations in a chemical reactor example.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/31933/1/0000886.pd

Inversion and zero dynamics in nonlinear multivariable control

This work concerns general multiple-input/multiple-output (MIMO) nonlinear systems with nonsingular characteristic matrix. For these systems, the problem of inversion is revisited and explicit formulas are derived for the full-order and the reduced inverse system. The reduced inverse naturally leads to an explicit calculation of the unforced zero dynamics of the system and the definition of a concept of forced zero dynamics. These concepts generalize the notion of transmission zeros for MIMO linear systems in a nonlinear setting. Chemical engineering examples are given to illustrate the calculation of zero dynamics. Input/output linearization is then interpreted as canceling the forced zero dynamics of the system, and precise internal stability conditions are derived for the closed-loop system.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/37419/1/690370406_ftp.pd