Differential Dynamic Programming for time-delayed systems

Trajectory optimization considers the problem of deciding how to control a dynamical system to move along a trajectory which minimizes some cost function. Differential Dynamic Programming (DDP) is an optimal control method which utilizes a second-order approximation of the problem to find the control. It is fast enough to allow real-time control and has been shown to work well for trajectory optimization in robotic systems. Here we extend classic DDP to systems with multiple time-delays in the state. Being able to find optimal trajectories for time-delayed systems with DDP opens up the possibility to use richer models for system identification and control, including recurrent neural networks with multiple timesteps in the state. We demonstrate the algorithm on a two-tank continuous stirred tank reactor. We also demonstrate the algorithm on a recurrent neural network trained to model an inverted pendulum with position information only.Comment: 7 pages, 6 figures, conference, Decision and Control (CDC), 2016 IEEE 55th Conference o

A study of the entanglement in systems with periodic boundary conditions

We define the local periodic linking number, LK, between two oriented closed or open chains in a system with three-dimensional periodic boundary conditions. The properties of LK indicate that it is an appropriate measure of entanglement between a collection of chains in a periodic system. Using this measure of linking to assess the extent of entanglement in a polymer melt we study the effect of CReTA algorithm on the entanglement of polyethylene chains. Our numerical results show that the statistics of the local periodic linking number observed for polymer melts before and after the application of CReTA are the same.Comment: 11 pages, 11 figure

Computer-assisted ex vivo, normothermic small bowel perfusion

Background: In the present study, a technique for computer-assisted, normothermic, oxygenated, ex vivo, recirculating small bowel perfusion was established as a tool to investigate organ pretreatment protocols and ischemia/reperfusion phenomena. A prerequisite for the desired setup was an organ chamber for ex vivo perfusion and the use of syngeneic whole blood as perfusate. Methods: The entire small bowel was harvested from Lewis rats and perfused in an organ chamber ex vivo for at least 2 h. The temperature was kept at 37 degrees C in a water bath. Three experimental groups were explored, characterized by different perfusion solutions. The basic perfusate consisted of syngeneic whole blood diluted with either NaCl, Krebs' solution or Krebs' solution and norepinephrine to a hematocrit of 30%. In addition, in each group l-glutamine was administered intraluminally. The desired perfusion pressure was 100 mm Hg which was kept constant with a computer-assisted data acquisition software, which measured an-line pressure, oxygenation, flow, temperature and pH and adjusted the pressure by changing the flow via a peristaltic pump. The viability of the preparation was tested by measuring oxygen consumption and maltose absorption, which requires intact enzymes of the mucosal brush border to break down maltose into glucose. Results: Organ perfusion in group 1 (dilution with NaCl) revealed problems such as hypersecretion into the bowel lumen, low vascular resistance and no maltose uptake. In contrast a viable organ could be demonstrated using Krebs' solution as dilution solution. The addition of norepinephrine led to an improved perfusion over the entire perfusion period. Maltose absorption was comparable to tests conducted with native small bower. Oxygen consumption was stable during the 2-hour perfusion period. Conclusions: The ex vivo perfusion system established enables small bowel perfusion for at least 2 h. The viability of the graft could be demonstrated. The perfusion time achieved is sufficient to study leukocyte/lymphocyte interaction with the endothelium of the graft vessels. In addition, a viable small bowel, after 2 h of ex vivo perfusion, facilitates testing of pretreatment protocols for the reduction of the immunogenicity of small bowel allografts. Copyright (C) 2000 S. Karger AG, Basel

Numerical renormalization-group study of spin correlations in one-dimensional random spin chains

We calculate the ground-state two-spin correlation functions of spin-1/2 quantum Heisenberg chains with random exchange couplings using the real-space renormalization group scheme. We extend the conventional scheme to take account of the contribution of local higher multiplet excitations in each decimation step. This extended scheme can provide highly accurate numerical data for large systems. The random average of staggered spin correlations of the chains with random antiferromagnetic (AF) couplings shows algebraic decay like $1/r^2$, which verifies the Fisher's analytic results. For chains with random ferromagnetic (FM) and AF couplings, the random average of generalized staggered correlations is found to decay more slowly than a power-law, in the form close to $1/\ln(r)$. The difference between the distribution functions of the spin correlations of the random AF chains and of the random FM-AF chains is also discussed.Comment: 14 pages including 8 figures, REVTeX, submitted to Physical Review

Localization length in Dorokhov's microscopic model of multichannel wires

We derive exact quantum expressions for the localization length $L_c$ for weak disorder in two- and three chain tight-binding systems coupled by random nearest-neighbour interchain hopping terms and including random energies of the atomic sites. These quasi-1D systems are the two- and three channel versions of Dorokhov's model of localization in a wire of $N$ periodically arranged atomic chains. We find that $L^{-1}_c=N.\xi^{-1}$ for the considered systems with $N=(1,2,3)$, where $\xi$ is Thouless' quantum expression for the inverse localization length in a single 1D Anderson chain, for weak disorder. The inverse localization length is defined from the exponential decay of the two-probe Landauer conductance, which is determined from an earlier transfer matrix solution of the Schr\"{o}dinger equation in a Bloch basis. Our exact expressions above differ qualitatively from Dorokhov's localization length identified as the length scaling parameter in his scaling description of the distribution of the participation ratio. For N=3 we also discuss the case where the coupled chains are arranged on a strip rather than periodically on a tube. From the transfer matrix treatment we also obtain reflection coefficients matrices which allow us to find mean free paths and to discuss their relation to localization lengths in the two- and three channel systems

Griffiths-McCoy singularities in random quantum spin chains: Exact results through renormalization

The Ma-Dasgupta-Hu renormalization group (RG) scheme is used to study singular quantities in the Griffiths phase of random quantum spin chains. For the random transverse-field Ising spin chain we have extended Fisher's analytical solution to the off-critical region and calculated the dynamical exponent exactly. Concerning other random chains we argue by scaling considerations that the RG method generally becomes asymptotically exact for large times, both at the critical point and in the whole Griffiths phase. This statement is checked via numerical calculations on the random Heisenberg and quantum Potts models by the density matrix renormalization group method.Comment: 4 pages RevTeX, 2 figures include