Control landscapes for a class of non-linear dynamical systems: sufficient conditions for the absence of traps

We establish three tractable, jointly sufficient conditions for the control landscapes of non-linear control systems to be trap free comparable to those now well known in quantum control. In particular, our results encompass end-point control problems for a general class of non-linear control systems of the form of a linear time invariant term with an additional state dependent non-linear term. Trap free landscapes ensure that local optimization methods (such as gradient ascent) can achieve monotonic convergence to effective control schemes in both simulation and practice. Within a large class of non-linear control problems, each of the three conditions is shown to hold for all but a null set of cases. Furthermore, we establish a Lipschitz condition for two of these assumptions; under specific circumstances, we explicitly find the associated Lipschitz constants. A detailed numerical investigation using the D-MOPRH control optimization algorithm is presented for a specific family of systems which meet the conditions for possessing trap free control landscapes. The results obtained confirm the trap free nature of the landscapes of such systems.Comment: 6 Figure

Dual time scales in simulated annealing of a two-dimensional Ising spin glass

We apply a generalized Kibble-Zurek out-of-equilibrium scaling ansatz to simulated annealing when approaching the spin-glass transition at temperature $T=0$ of the two-dimensional Ising model with random $J= \pm 1$ couplings. Analyzing the spin-glass order parameter and the excess energy as functions of the system size and the annealing velocity in Monte Carlo simulations with Metropolis dynamics, we find scaling where the energy relaxes slower than the spin-glass order parameter, i.e., there are two different dynamic exponents. The values of the exponents relating the relaxation time scales to the system length, $\tau \sim L^z$, are $z=8.28 \pm 0.03$ for the relaxation of the order parameter and $z=10.31 \pm 0.04$ for the energy relaxation. We argue that the behavior with dual time scales arises as a consequence of the entropy-driven ordering mechanism within droplet theory. We point out that the dynamic exponents found here for $T \to 0$ simulated annealing are different from the temperature-dependent equilibrium dynamic exponent $z_{\rm eq}(T)$, for which previous studies have found a divergent behavior; $z_{\rm eq}(T\to 0) \to \infty$. Thus, our study shows that, within Metropolis dynamics, it is easier to relax the system to one of its degenerate ground states than to migrate at low temperatures between regions of the configuration space surrounding different ground states. In a more general context of optimization, our study provides an example of robust dense-region solutions for which the excess energy (the conventional cost function) may not be the best measure of success.Comment: 13 pages, 16 figure

Design of coherent quantum observers for linear quantum systems

Quantum versions of control problems are often more difficult than their classical counterparts because of the additional constraints imposed by quantum dynamics. For example, the quantum LQG and quantum H infinity optimal control problems remain open. To make further progress, new, systematic and tractable methods need to be developed. This paper gives three algorithms for designing coherent observers, i.e., quantum systems that are connected to a quantum plant and their outputs provide information about the internal state of the plant. Importantly, coherent observers avoid measurements of the plant outputs. We compare our coherent observers with a classical (measurement-based) observer by way of an example involving an optical cavity with thermal and vacuum noises as inputs.Comment: 21 pages, 9 figure

Dynamic scaling in the 2D Ising spin glass with Gaussian couplings

We carry out simulated annealing and employ a generalized Kibble-Zurek scaling hypothesis to study the 2D Ising spin glass with normal-distributed couplings. The system has an equilibrium glass transition at temperature $T=0$. From a scaling analysis when $T\rightarrow 0$ at different annealing velocities, we extract the dynamic critical exponent $z$, i.e., the exponent relating the relaxation time $\tau$ to the system length $L$; $\tau\sim L^z$. We find $z=13.6 \pm 0.4$ for both the Edwards-Anderson spin-glass order parameter and the excess energy. This is different from a previous study of the system with bimodal couplings [S. J. Rubin, N. Xu, and A. W. Sandvik, Phys. Rev. E {\bf 95}, 052133 (2017)] where the dynamics is faster and the above two quantities relax with different exponents (and that of the energy is larger). We here argue that the different behaviors arise as a consequence of the different low-energy landscapes---for normal-distributed couplings the ground state is unique (up to a spin reflection) while the system with bimodal couplings is massively degenerate. Our results reinforce the conclusion of anomalous entropy-driven relaxation behavior in the bimodal Ising glass. In the case of a continuous coupling distribution, our results presented here indicate that, although Kibble-Zurek scaling holds, the perturbative behavior normally applying in the slow limit breaks down, likely due to quasi-degenerate states, and the scaling function takes a different form.Comment: 10 pages, 5 figure

Evaluation of Brushing as a Lunar Dust Mitigation Strategy for Thermal Control Surfaces

Evaluation of brushing to remove lunar simulant dust from thermal control surfaces is described. First, strip brushes made with nylon, PTFE, or Thunderon bristles were used to remove JSC-1AF dust from AZ93 thermal control paint or aluminized FEP (AlFEP) thermal control surface under ambient laboratory conditions. Nylon and PTFE bristles removed a promising amount of dust from AZ93, and nylon and Thunderon bristles from AlFEP. But when these were tested under simulated lunar conditions in the lunar dust adhesion bell jar (LDAB), they were not effective. In a third effort, seven brushes made up of three different materials, two different geometries, and different bristle lengths and thicknesses were tested under laboratory conditions against AZ93 and AlFEP. Two of these brushes, the Zephyr fiberglass fingerprint brush and the Escoda nylon fan brush, removed over 90 percent of the dust, and so were tested in the fourth effort in the LDAB. They also performed well under these conditions recovering 80 percent or more of the original thermal performance (solar absorptance/thermal emittance) of both AZ93 and AgFEP after 20 strokes, and 90 or more percent after 200 strokes

Hubungan Antara Asupan Protein Dan Zat Besi Dengan Kadar Hemoglobin Mahasiswa Program Studi Pendidikan Dokter Angkatan 2013 Fakultas Kedokteran Universitas Sam Ratulangi

: Hemoglobin is the oxygen-carrying compound in red blood cells. Someone hemoglobin level scan be affected by several other factors: age, gender, systemic disease and diet. Nutrient intake plays a role in the formation of redblood cells. Disruption of the formation of redblood cells could be due to lack of food consumed contains essential nutrients such as iron, folic acid, vitamin B12, protein, vitamin C and other important nutrients. This study aims to determine the relation ship between the intake of protein and iron in hemoglobin level student of medical education force in 2013 Sam Ratulangi University School of Medicine. The design is an analytical study using cross-sectional approach. The study sample is determined and carried out systematic random sampling proportional to the gender of men and women and who met the inclusion criteria sample amounted to75 people. Data were collected through questionnaires and food recall by measuring hemoglobin levels, then the data were analyzed using the Spearman rank test. Protein intake is less 52.0%, 16.0% protein and enough protein intake over 32.0%. Iron intake less than 98.7% and 1.3% more protein intake. Normal hemoglobin levels of 93.3% and 6.7% is not normal. Conclusion: The results of the study with Spearman rank test for protein and hemoglobin levels obtained p-value is 0.138 (p>α=0.05) which means that there is no significant relationship between iron intake with hemoglobin levels. For intake of iron and hemoglobin levels obtained p value is 0.198 (p>α=0.05), which means there is nosignificant relationship between iron intake with hemoglobin levels

Irreversible Performance of a Quantum Harmonic Heat Engine

The unavoidable irreversible losses of power in a heat engine are found to be of quantum origin. Following thermodynamic tradition a model quantum heat engine operating by the Otto cycle is analyzed. The working medium of the model is composed of an ensemble of harmonic oscillators. A link is established between the quantum observables and thermodynamical variables based on the concept of canonical invariance. These quantum variables are sufficient to determine the state of the system and with it all thermodynamical variables. Conditions for optimal work, power and entropy production show that maximum power is a compromise between the quasistatic limit of adiabatic following on the compression and expansion branches and a sudden limit of very short time allocation to these branches. At high temperatures and quasistatic operating conditions the efficiency at maximum power coincides with the endoreversible result. The optimal compression ratio varies from the square root of the temperature ratio in the quasistatic limit where their reversibility is dominated by heat conductance to the temperature ratio to the power of 1/4 in the sudden limit when the irreversibility is dominated by friction. When the engine deviates from adiabatic conditions the performance is subject to friction. The origin of this friction can be traced to the noncommutability of the kinetic and potential energy of the working medium.Comment: 25 pages, 7 figures. Revision added explicit heat-transfer expression and extended the discussion on the quantum origin of frictio

Thermodynamics of MHD flows with axial symmetry

We present strategies based upon extremization principles, in the case of the axisymmetric equations of magnetohydrodynamics (MHD). We study the equilibrium shape by using a minimum energy principle under the constraints of the MHD axisymmetric equations. We also propose a numerical algorithm based on a maximum energy dissipation principle to compute in a consistent way the equilibrium states. Then, we develop the statistical mechanics of such flows and recover the same equilibrium states giving a justification of the minimum energy principle. We find that fluctuations obey a Gaussian shape and we make the link between the conservation of the Casimirs on the coarse-grained scale and the process of energy dissipation